Four-Sided Dice A pair of four-sided dice-each with the numbers from 1 to 4 on their sides- -are rolled, and the num bers facing down are observed. (Note: A four-sided die is sim- ilar to a pyramid with a triangular base.) (a) List the sample space. (b) Describe each of the following events as a subset of the sample space i) Both numbers are even. (ii) At least one number is odd. iii Neither number is less than or equal to 2. (iv) The sum of the numbers is 7. (v) The sum of the numbers is greater than or equal to 6. (vi) The numbers are the same. (vii) A 2 or 3 occurs, but not both 2 and 3. (viii) No 4 appears.
Previous question

Answers

Answer 1

Answer:

Step-by-step explanation:

(a)

The sample space is

{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}

(b)

i  {(2,2), (4,4), (2,4), 4,2)}

ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}

iii {(1,1)}

iv {3,4), (4,3)}

v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}

vi {(1,1), (2,2), (3,3), (4,4)}

vii  {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}

viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}


Related Questions

researchers hoped to determine whether time spent watching television is associated with cardiovascular fitness. subjects were asked how many hours per day they watch television and were classified as physically fit if they scored in the excellent or very good category on a step test. the data obtained is as follows:

Answers

A hypothesis Test will be used to check the association the researchers were interested in exist or not. Chi-square test statistic will be used for testing the relationship between gender and participation in the last election.

The hypothesis test we shall use here is -

Chi-square test for independence

Reason - this type of hypothesis test is used to test whether there is a significant association between two categorical variables.

The two variables in this question are hours spent watching TV and cardiovascular fitness.

2.) Test statistic here is

Chi-square test statistic

Reason - here also to test the association we should use the chi-square test for

and thus the test statistic would be Chi-square.

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Find the coordinates of the circumcenter of the triangle with the given vertices.
A(2, 2), B(2, 4), C(8, 4)
The circumcenter is (_ ,_)

Answers

The circumference of the triangle is 14.3 Units

How to find the circumference?

We know that a triangle is a polygon that has three sides, three angles and three vertices whose sum of interior angles is 180 degrees.

The coordinates of the given  vertices are:

A(2,2)

B(2,4)

C(8,4)

To find the sides of the triangle, we use the formula for distance between two points

/AB/=[tex]\sqrt{(X_{2}-X_{1}) ^{2} +(Y_{2} -Y_{1})^{2} }[/tex]

= applying the figures in the formula we have

[tex]\sqrt{(2-2)^{2}+(2-4)^{2} }[/tex]

AB=√0+4

AB=2 Units

Applying the formula for /AC/

/AC/=[tex]\sqrt{(2-8)^{2}+(2-4)^{2} }[/tex]

simplifying to have

√40

/AC/=6.6 Units

Applying the formula for /BC/

/BC/=[tex]\sqrt{(8-2)^{2} +(4-4)^{2}[/tex]

/BC/=√36

/BC/=6

Therefore, the circumference of the triangle is 2+6+6.3

= 14.3 units

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A college admissions officer for an MBA program has determined that historically
applicants have undergraduate grade point averages that are normally distributed with
standard deviation 0.45. From a random sample of 25 applications from the current year,
the sample mean grade point average is 2.90.
Required: Find the confidence interval foe the population mean at the 5% significance level.
(10marks)
B. An educational study was designed to investigate the effectiveness of a reading program
of elementary age children. Each child was given a pre-test and post-test. Higher posttest scores would indicate reading improvement. From a very large population, a random
sample of scores for the pre-test and post-test are as follows:

Answers

The confidence interval for the population mean at significance level is

2.724<μ<30.76 .

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Population standard deviation: σ = 0.45

Sample size: n = 25

Sample Mean: x= 2.90

Х=2.90 represent the sample mean for the sample  

μ population mean (variable of interest)

σ = 0.45 represent the population standard deviation

n=25 represent the sample size  

We have the following distribution for the random variable:

X≈N(μ,σ =0.45)

And by the central theorem we know that the distribution for the sample mean is given by:

X≈N( μ, [tex]\frac{σ}{\sqrt{n} }[/tex])

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha =0.05[/tex] and[tex]\frac{\alpha }{2} =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)" and we see that

Z₁ =±1.96

Now we have everything in order to replace into formula:

[tex]2.90-1.96\frac{0.45}{\sqrt{25} }=2.724[/tex]

[tex]2.90+1.96\frac{0.45}{\sqrt{25} }=3.076[/tex]

So on this case the 95% confidence interval would be given by (2.724:3.076) .

At a significance level, the population mean's confidence interval is 2.724–30.76.

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Solve the given problem related to population growth. During the first decade of this century, the population of a certain city grew exponentially. The population of the city was 145,210 in 2000 and 219,185 in 2010. Find the exponential growth function that models the population growth of the city. Use t = 0 to represent 2000, t - 10 to represent 2010, and so on. (Round k to five decimal places.) N(C) = Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Answers

The exponential growth function that models the population growth of the given city is P(t) = P(0) x e^rt and the population of the city in 2016 is 328,029.39.

The population of the city in 2000 (t=0) = 145,210

The population of the city in 2010 (t=10) = 219,185

Rate of growth for 10 years = ((219185 - 145210)/145210) x 100

Rate of growth for 10 years = 50.943%

Rate of growth per year = Rate of growth for 10 years/10

Rate of growth per year = (50.943/10)%

Rate of growth per year = 5.094%

According to the exponential growth function,

P(t) = P(0) x e^rt

Population in 2016 (t=16) is:

P(16) = 145210 x e^((5.094/100) x 16)

P(16) = 145210 x 2.259

P(16) = 328029.39

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Write the equation of the line, in slope-intercept form, with the following information: slope:-1/12 point: (36, 2)​

Answers

Answer:

y = - 1/12x + 5

------------------------------------

Use point-slope form first and convert to slope-intercept.

Point-slope form:

y - y₁ = m(x - x₁), where (x₁, y₁) is a point and m- slope

Slope-intercept form:

y = mx + b, where m- slope, b- y-intercept

Plug in the values:

y - 2 = - 1/12(x - 36)y - 2 = - 1/12x + 3y = - 1/12x + 3 + 2y = - 1/12x + 5

Answer:

y = - 1/12x + 5

Step-by-step explanation:

Two pieces of metal measure one and one third yards and five sixths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed? one and one half yards, 2 yards, four and one third yards, six and one half yards.
Pls help

Answers

Answer: 6 1/2 yards

Step-by-step explanation: you have to add 1 1/3 + 5/6, which is 2 1/6. 2 1/6x3=6 1/2

If the probability that a person will die in the next year is
probability that the person will not die in the next year?
OA. 99%
B. 99548
C. 0.00452
OD. 0.99548
452
100,000
what is the
SUBMIT

Answers

The probability that the person will not die will be D. 0.99548

How to illustrate the probability?

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

Since the probability that the person will die is 814/1000000, the probability that the person will not die will be:

= 1 - 452/100000

= 99548/100000

= 0.99548

The correct option is D.

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If the probability that a person will die in the next year is 452/100000, the probability that the person will not die in the next year?

A. 99%

B. 0.99548

C. 0.00452

D. 0.99548

An infant drinks about 28 ounces of milk per day. About how many quarts of milk does the baby drink in 4 weeks?
options 49 qt 7 qt 32 qt 24.5 qt

Answers

An infant drinks about 28 ounces of milk per day. There are 32 ounces in a quart, so the baby drinks 28 ÷ 32 = 0.875 quarts of milk per day.

Four weeks is 4 × 7 = 28 days.

In 4 weeks, the baby drinks 28 × 0.875 = 24.5 quarts of milk.

for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df -

Answers

for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df - 2(3-1)=2

The Kruskal-Wallis test statistic has a degrees of freedom (df) equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1).The Kruskal-Wallis test statistic is a non-parametric test used to compare the means of a set of independent samples. In this case, we have three separate samples of n-10 for each treatment. To calculate the Kruskal-Wallis test statistic, we need to first calculate the sum of the ranks for each sample and then subtract the expected sum of ranks for each sample. The df for the Kruskal-Wallis test statistic is equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1). Finally, the Kruskal-Wallis test statistic is calculated by dividing the calculated sum of ranks by the expected sum of ranks and multiplying by the df. This will give us the Kruskal-Wallis test statistic for the data set.

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I don’t know why I’m finding this so hard but I’ve tried so many attempts

Answers

Check the picture below.

pls help asap I will give many points just help me on this​

Answers

Answer:1=t

2=flase

3=flase

4=flase

5=true

6=true

7flase

8=true

Step-by-step explanation:i spelt false wrong lol

greed. bad luck. failing to treat each throw of the dice as independent of previous throws. treating each throw of the dice as independent of previous throws. regression toward the mean.

Answers

The Gambler's Fallacy is due to treating each throw of the dice as independent of previous throws

The gambler's fallacy, also known as the Monte Carlo fallacy, is when someone mistakenly thinks that the outcome of a prior event or series of events will make a given random occurrence more or less likely to occur.

This kind of thinking is flawed since past occurrences do not alter the likelihood that specific events will occur in the future.

In circumstances where the probability of various events is not independent, the gambler's fallacy is not applicable.

The outcome of previous events, such as the statistical permutation of events, might alter the probability of future happenings in such circumstances.

In response to the query,

The Gambler's Fallacy results from treating each roll of the dice as if it were unrelated to prior rolls. Option(4) is correct

The question is incomplete , the complete question is

The Gambler's Fallacy is due to

(1) greed.

(2) bad luck.

(3) failing to treat each throw of the dice as independent of previous throws.

(4) treating each throw of the dice as independent of previous throws.

(5) regression toward the mean.

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DEATH RACE FOR LOVE 999
In 1941, the ________ was signed by Great Britain and the United States, stating that neither country wanted to acquire territory nor would attempt to govern other nations.

Marshall Plan
United Nations Charter
Truman Doctrine
Atlantic Charter

Answers

Answer:

Step-by-step explanation:

D. Atlantic Charter

The Atlantic Charter established the creation of the United Nations.

Which sequence explains a geometric method of determining
● Plot 2 + 2i. Scale by 2. Rotate 45° clockwise.
4
Plot 3-17i. Scale by ✓2.Rotate 45° clockwise.
O Plot 2 + 2i. Scale by 2√2. Rotate 45° clockwise.
Plot 3-17i. Scale by 2√2. Rotate 45° clockwise.
3-171 ?
2 + 2i

Answers

Answer:

Second option (Plot 3-17i. Scale by ✓2/4 .Rotate 45° clockwise.)

Step-by-step explanation:

Given below in the picture.

I hope my answer helps you.

a random sample of adults was surveyed about their exercise habits. of the 100 surveyed, 56 stated they exercise regularly. which of the following is the 95% confidence interval for p, the proportion of all adults who exercise regularly? find the z-table here. (0.50, 0.62) (0.48, 0.64) (0.46, 0.66) (0.43, 0.69)

Answers

The 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given

Sample size(n) = 100

x = 56

Sample proportion (p) = x/n = 56/100 = 0.56

Here, c =  95%, a = 0.95

1-a = 0.05, a/2 = 0.025

Z(a/2) = 1.96

95% confidence interval for p is:

= p-Z(a/2)√{p(1-p)}/n, p+Z(a/2)√{p(1-p)}/n

= 0.56- 1.96√{0.56(1-0.56)}/100, 0.56+1.96√{0.56(1-0.56)}/100

= 0.56 - 0.0972, 0.56+0.0972

= 0.4628, 0.6572

= (0.46, 0.66)

Hence, the 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).

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y = x^4 , y = 2 − |x|

Answers

Answer:

no solution

y=x^3

y= 2-1 x 1

Step-by-step explanation:

1. Computer Depot is a large store that sells and repairs computers. A random sample of 110 computer repair jobs took technicians an average of = 93.2 minutes per computer. Assume that  is known to be 16.9 minutes.
(a) Find a 99% confidence interval for the population mean time  for computer repairs.
(b) Write a brief explanation of the meaning of the confidence interval in the context of this problem.

Answers

Confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].

What is confidence interval?

A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for an exact proportion of times.

Main body:

According to question:

N = 110

X bar = 93.9 minutes

σ = 16.9 minutes

value for 99% confidence interval = 2.576

C.I. = x bar ± z*s/√n

C.I. = 93.9 ± 2.576 *16.9 /√110

C.I. = 93.9 ± 4.150

C.I. = [98.05 , 89.850]

Hence , confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].

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A property is available for sale that could normally be financed with a fully amortizing $82,800 loan at a 10 percent rate with monthly payments over a 25-year term. Payments would be $752.40 per month. The builder is offering buyers a mortgage that reduces the payments by 50 percent for the first year and 25 percent for the second year. After the second year, regular monthly payments of $752.40 would be made for the remainder of the loan term.



Required:

a. How much would you expect the builder to have to give the bank to buy down the payments as indicated?

b. Would you recommend the property be purchased if it was selling for $5,000 more than similar properties that do not have the buydown available?

Answers

The builder must pay the bank $6005.66. for further details read below.

what is the mortgage?

A mortgage is a type of loan used to purchase or maintain a home, land, or other types of real estate.

For the given problem We must determine the present value of all the relaxations granted to us over the first two years in order to determine how much the builder must pay the bank for this buydown payment. The output and Excel formulae are listed below.

Monthly payment    726.96

Monthly interest rate   10.%/12

Relaxation value in 1st year:

Amount reduced     C2*50%

No. of months    12

present value    PV(C3,C7, -C6)

Relaxation value in 2nd year:

The amount reduced       C2*25%

No. of months    12

present value    PV(C3,C12, -c11)

Present value today     C13/(1+ C 3)^12

Present value of buy option     C14 + C8

Therefore, the buydown option's current value is $6005.66. In order to provide this option to the customers, the builder must pay the bank $6005.66.

b. It is advised to take advantage of this option since the benefit the house buyer would get, or its current value exceeds the additional cost. Benefits to the purchaser of this option include. The benefit to the buyer equals the Present Value of the BuyDown Option - Additional Payment

Buyer benefit is equal to 6005.66 - 5000, or 1005.66$.

So, if a buyer received this option, he would profit $1005.66. It is thus advised to purchase real estate using this buydown option.

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Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error. Round your answers to three significant figures.)
cos(0.3)=1−(0.3)22!+(0.3)44!
R4≤ .
R4=.

Answers

Answer:

Step-by-step explanation:

According to Tylor theorem,

f(x)=f(a)+f′(a)/1!×(x−a)+f′′(a)/2!×(x−a)2+......+fn(a)/n!×(x−a)n

Tylor series for cosx is

1 - x^2/2! + x^4/4! + x^6/6! + ……

cos (0.3) = 1 - 〖(0.3)〗^2/2! + 〖(0.3)〗^4/4!

The R4 valur is fourth derivative of cosx

f’(x) = -sinx

f’’ (x) = -cosx

f’’’ (x) = sinx

f’’’’ (x) = cosx

Here, a = 0, n = 3, x = 0.3

max l f^4l = cos (0.3)

               = 0.9999

lR_4  (x)l ≤ |0.3-0|^(4+1)/4! × 0.9999

              ≤ 0.00015186

               = 1.51786 × 10^(-4)

R_n (x) = cos (0.3) – (1 - 〖(0.3)〗^2/2!-(0.3)^4/4!)

          = 0.0446

The error of approximation R_4  (x) ≤ 1.2 × 10^(-2) and exact value of error R_4 = 0.0446

Element X is a radioactive isotope such that every 71 years, its mass decreases by half.
Given that the initial mass of a sample of Element X is 30 grams, write a function
showing the mass of the sample remaining after t years, where the annual decay rate
can be found from a constant in the function. Round all coefficients in the function to
four decimal places. Also, determine the percentage rate of decay per year, to the
nearest hundredth of a percent.

Answers

1) The function that shows the decay is N(t) = 30e^-rt.

2) The percentage rate of decay is 0.98 %.

What is the function?

We know that an element is said to be radioactive if the element can be able to decay spontaneously. The implication of this is that the amount of the element that in the system would continue to be reduced and new daughter nuclei are formed.

We have that;

If the initial mass of the radioactive isotope X has been give to us in the question as 30 g then it follows that we can write the function as;

N(t) = 30e^-rt

N(t) =Mass of the element at time t

r = rate of decay

t = time taken

Since half of the element X would remain after 71 years, we have;

15 = 30e^ -71r

15/30 = e^ -71r

0.5 = e^ -71r

ln 0.5 = -71r

r = ln 0.5/-71

r = 0.0098 or 0.98 %

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Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years: Number of years 1 2 3 House 1 (value in dollars) 294,580 303,417.40 312,519.92 House 2 (value in dollars) 295,000 304,000 313,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

Answers

a) The type of function that can be used to describe the value of each house is:

House 1: Exponential function.House 2: Linear function.

b) The functions that define the value of each house are given as follows:

House 1: H1(x) = 294580(1.03)^x.House 2: H2(x) = 295,000 + 9,000x.

What are the functions?

For House 1, the change each year is a percentage, as follows:

312519.92/303417.30 = 303417.30/294580 = 1.03.

Hence, considering the initial value of $294,580, the exponential function is defined as follows:

H1(x) = 294580(1.03)^x.

For House 2, the change each year is a fixed amount, as follows:

313,000 - 304,000 = 304,000 - 295,000 = 9,000.

Hence, considering the initial value of 295,000, the linear function is defined as follows:

H2(x) = 295,000 + 9,000x.

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Work out m and c for the line: y = 3-4x​

Answers

Answer:

m = -4 ; c = 3

Step-by-step explanation:

m is the number that multiplies x


c is the number without letters

0.1 recurring as a fraction

Answers

Answer:

1/9

Step-by-step explanation:

PLEASE MARK AS BRAINLIEST

Surwatullah is starting university in 3 years and would like to have $4000 when he starts. He has $3000 to invest now, and his bank pays 5% compounded quarterly. Will he have enough?

Answers

Answer:

Answer found by the following formula/e: CI = A – P

none of the answer choices is correct. the sample consisted of all veterinarians who treat horses with nsaids. the sample consisted of all veterinarians on the list and therefore equaled the target population. the sample consisted of all veterinarians who returned the questionnaire.

Answers

equaled the target population. the sample consisted of all veterinarians who returned the questionnaire is None of the answer choices is correct.

The sample in this case consists of all veterinarians who treat horses with Non-Steroidal Anti-Inflammatory Drugs (NSAIDs). The target population for this study would be all veterinarians who treat horses with NSAIDs. Therefore, since the sample is made up of all veterinarians in the target population, the sample equals the target population. None of the answer choices provided is correct in this scenario.

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A phone company charge a base fee of $12 per month plus additional charge per minute. The monthly phone cost can be represented by the following equation where is the additional charge per minute and is the number of minutes used. Rearrange the equation to solve for the number of minutes, m.

C=12+a•m

Answers

m=(C-12)/a

According to question

C=12+a*m

⇒C-12=a*m

⇒(C-12)/a=m

∴Equation to solve for the number of minutes , m = (C-12)/a

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Which function has the same graph as f(x) = 0.3|x|?

Answers

Answer:

D

Step-by-step explanation:

b/c

A B and C are not true

Answer:

D

Step-by-step explanation:

We can visualize this by ignoring the constant of 0.3 and remembering the |x| graph.

It has a -x slope when x < 0, and a +x slope when x > 0

The only answer that has a negative slope when x is less than 0 and a positive slope when x is greater than 0 is D.

Mackenzie's car used 4 gallons to travel 108 miles. How many gallons of gas would she need to travel 162 miles?

Answers

The gallons of gas that she would need to travel 162 miles will be 4374 gallons.

How to illustrate the ratio?

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mackenzie's car used 4 gallons to travel 108 miles. The rate will be:

= 108 / 4

= 27 miles per gallon

The gallons of gas that she would need to travel 162 miles will be:

= 162 × 27

= 4374 gallons.

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Assume that the distributions for the following scenarios are normal. Use the normal standard table to find the following probabilities. Round z-scores to the nearest hundredth.
1. The average score on a math test is 75 with a standard deviation of 8. What is the probability that a randomly selected test has a score of 90 or higher?

2. The life of a gas grill is 3.5 years with a standard deviation 0.35 years. What is the probability that the grill will last less than 3 years?

3. Ambulance response times average 7.5 minutes with a standard deviation of 2.5. What is the probability that an ambulance will respond within 6 to 8 minutes.

Answers

Answer:

1. To find the probability that a randomly selected test has a score of 90 or higher, we need to find the z-score corresponding to a score of 90 and then use the standard normal table to find the probability that a score is greater than or equal to this value. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the score we are interested in, mean is the average score, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z = (90 - 75) / 8 = 1.875

Rounding this value to the nearest hundredth, we get z = 1.88. Looking up this value in the standard normal table, we find that the probability that a score is greater than or equal to 1.88 is 0.9637. Therefore, the probability that a randomly selected test has a score of 90 or higher is 0.9637.

2. To find the probability that the grill will last less than 3 years, we need to find the z-score corresponding to a life of 3 years and then use the standard normal table to find the probability that a life is less than this value. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z = (3 - 3.5) / 0.35 = -1.43

Rounding this value to the nearest hundredth, we get z = -1.43. Looking up this value in the standard normal table, we find that the probability that a life is less than -1.43 is 0.0747. Therefore, the probability that the grill will last less than 3 years is 0.0747.

3. To find the probability that the ambulance will respond within 6 to 8 minutes, we need to find the z-scores corresponding to a response time of 6 and 8 minutes, respectively, and then use the standard normal table to find the probability that a response time is between these two values. To find the z-score, we can use the formula:

z = (x - mean) / standard deviation

where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:

z1 = (6 - 7.5) / 2.5 = -0.6

z2 = (8 - 7.5) / 2.5 = 0.2

Rounding these values to the nearest hundredth, we get z1 = -0.6 and z2 = 0.2. Looking up these values in the standard normal table, we find that the probability that a response time is less than -0.6 is 0.2743 and the probability that a response time is less than 0.2 is 0.5398. Therefore, the probability that a response time is between -0.6 and 0.2 is 0.5398 - 0.2743 = 0.2655. Therefore, the probability that the ambulance will respond within 6 to 8 minutes is 0.2655.

1. The probability that a randomly selected test has a score of 90 or higher is 0.0301.

2. The probability that the grill will last less than 3 years is 0.0764.

3. The probability that an ambulance will respond within 6 to 8 minutes is 0.1465.

How to determine the required probabilities?

In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:

Z-score, z = (x - μ)/σ

Where:

σ represents the standard deviation.x represents the sample score.μ represents the mean score.

Part 1.

By substituting the given parameters, we have the following:

Z-score, z = (90 - 75)/8

Z-score, z = 1.88

Based on the standardized normal distribution table, the required probability is given by:

P(Z ≥ 1.88) = 1 - P(x < Z)

P(Z ≥ 1.88) = 1 - 0.9699

Probability = 0.0301.

Part 2.

By substituting the given parameters, we have the following:

Z-score, z = (3 - 3.5)/0.35

Z-score, z = -1.43

Based on the standardized normal distribution table, the required probability is given by:

P(Z < -1.43) = 1 - P(x > Z)

P(Z < -1.43) = 1 - 0.9236

Probability = 0.0764.

Part 3.

At 6 minutes, we have:

Z-score, z = (6 - 7.5)/2.5

Z-score, z = -0.6

At 8 minutes, we have:

Z-score, z = (8 - 7.5)/2.5

Z-score, z = 0.2

Based on the standardized normal distribution table, the required probability is given by:

P(6 < x < 8) = P(-0.6 < z < 0.2)

P(-0.6 < z < 0.2) = P(z < 0.2) - P(z < -0.6)

P(-0.6 < z < 0.2) = 0.42074 - 0.27425

P(-0.6 < z < 0.2) = 0.1465.

Read more on z-score here: brainly.com/question/26714379

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A square-based pyramid has a total of five faces. Four of the faces are triangles and one of the faces is a square. The surface area of a square-based pyramid is the total area of all its sides.

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