The graph of a function is shown below. What is true about the function on the interval -5< x < -2?

Answer:

2 × 2 × 7

Step-by-step explanation:

start dividing by the lowest prime and work up until 1 is reached

28 ÷ 2 = 14

14 ÷ 2 = 7

7 ÷ 7 = 1

then

28 = 2 × 2 × 7 = 2² × 7

In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1

What is standard deviation?

In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary

Main body:

The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.

Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.

Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.

The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).

The sigma value for the standard normal Z distribution is sigma = 1

sigma = population standard deviation

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a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.

b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.

The ordered pair for the vertices after the transformation will be:

Q' = (3, 5)

R' = (5, -1)

S'= (2, 0)

T' = (0, 3)

A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.

Given:  (Ry-axis T(2, 0))(QRST). That means we have a translation T(2, 0). This implies (x,y) → (x + 2, y + 0). Thus, the ordered pair for the vertices will be:

Q (x = 1, y = 5)

Q' = Q(x+2, y + 0) = (1+2, 5+0) = (3, 5)

R (x = 3, y = -1)

R' = R(x+2, y + 0) = (3+2, -1+0) = (5, -1)

S (x = 0, y = 0)

S' = S(x+2, y + 0) = (0+2, 0+0) = (2, 0)

T (x = -2, y = 3)

T' = T(x+2, y + 0) = (-2+2, 3+0) = (0, 3)

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Check the picture below.

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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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.

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

Step-by-step explanation:

so, we have 1 position with 2 options (0 or 1).

and 6 positions with 10 options (0 to 9).

so, we have

2×10×10×10×10×10×10 = 2×10⁶ = 2,000,000

different identification numbers possible.

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.

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:

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.

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We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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To write the equation in exponential form we must follow certain rules:

1. Logarithm product rule -            log b ( x ∙ y) = log b ( x) + log b ( y)

2. Logarithm quotient rule -           log b ( x / y) = log b ( x) - log b ( y)

3. Logarithm power rule -               log b ( x y) = y ∙ log b ( x)

4. Logarithm base switch rule -     log b ( c) = 1 / log c ( b)

1. ㏒z(w) = p

Here all constants are taken to be positive and not equal to 1

z = base of the logarithmic function

z^p = w --------> (1)

This z^p = w is the exponential form of ㏒z(w) = p

2. ㏒(s) = r

Here all constants are taken to be positive and not equal to 1

e = base of the logarithmic function

e^r = s --------> (2)

This e^r = s is the exponential form of ㏒(s) = r

3. 7m = a

Here we have to write the equation in logarithmic form

㏒(7m) = log r

log(7m) - log r = 0

We know quotient rule :-

log b ( x / y) = log b ( x) - log b ( y)  --------(A)

Applying that same principle to our question by using this equation we have:

log (7m/r)

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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

Answer: Brazil and Alaska

Step-by-step explanation

Take away Brazil's temperature from Alaska's to get your answer

81 - 23 = 58'F

The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)

consider A=(2,5)

To find the polar coordinates we have the formula:

[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]

Assume that x=2,y=5 and substitute in equation(1)

r=√2^2+5^2 and tan^-1(5/2)

r=√4+25 and tan^-1(2.5)

r=(√29,68.1°)

For point B =(3,-6)

Assume that x=3,y=-6 and substitute in equation(1)

r=√3^3+(-6)^2 and tan^-1(-6/2)

r=√9+36 and tan^-1(-2)

r=(√45,-63.9°)

For point C=(-4,9)

Assume that x=-4,y=9 and substitute in equation(1)

r=√(-4)^2+9^2 and tan^-1(9/-4)

r=√16+81 and tan^-1(2.25)

r=(√97,66.0°)

For the point D=(-8,-1)

Assume that x=-8,y=-1 and substitute in equation(1)

r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)

r=√64+1 ,7.12°

r=(√65,7.12°)

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Answer:

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

Simplify:

Answer:

[tex] \sf \red{c) \: 16} \: is \: the \: answer.[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf →6 + \frac{3}{8} [/tex]

Changing error in problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

Let's solve the problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

[tex] \sf →6 \times \frac{8}{3} [/tex]

[tex] \sf → \frac{(6 \times 8)}{3} [/tex]

[tex] \sf → \frac{48}{3} [/tex]

[tex] \sf \: →16 \:[/tex]

Hence, the answer is 16.

The function represented by the series is [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

The interval of convergence of the series is ( - 1, 1 )

As per the question the given function is:

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$[/tex]

[tex]$$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$[/tex]

[tex]$$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$[/tex]

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$[/tex]

Thus, [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$[/tex]

[tex]$$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$[/tex]

The series will converge, if L<1

[tex]$$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}[/tex]

[tex]& x^2 < 1 \\[/tex]

 |x| < 1

 -1 < x < 1

Substitute the values of 'x' in the given function

At, x = - 1

[tex]\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$[/tex]

Also, at x = 1

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$[/tex]

Thus, the interval of convergence is ( - 1, 1 )

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We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets. The correspondence a function.

The symbol for an ordered pair is (INPUT, OUTPUT): The relation denotes the connection between the input and output.

For the stated question-

We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets.

One student is related to one facility.

Thus, correspondence given forms a function.

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Answer:

1/9

Step-by-step explanation:

PLEASE MARK AS BRAINLIEST

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

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

Hello,

The probability that both number generators generate the number 5 is (1/10) * (1/10) = 1/100 = 0.01 or 1%.

This is because the probability of an event occurring is the product of the probabilities of each event occurring independently. In this case, the probability of the first generator generating the number 5 is 1/10 and the probability of the second generator generating the number 5 is also 1/10, so the probability of both events occurring is (1/10) * (1/10) = 1/100.

----

Answer:

A. x = -6

Step-by-step explanation:

-1/6x - 5 = 2/3x

add 1/6x to both sides:

-1/6x - 5 + 1/6x = 2/3x + 1/6x

-5 = 2/3x + 1/6x

common denominator on right side:

-5 = 4/6x + 1/6x

combine right side:

-5 = 5/6x

multiply both sides by 6/5:

(-5)(6/5) = (5/6x)(6/5)

-30/5 = x

reduce left side:

-6 = x

x = -6 (option a)

Answer: A) x=-6

Step by step explanation:

[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x }}[/tex]

We calculate the multiplication expression.

    [tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x \iff \ -\dfrac{x}{6}-5=\dfrac{2}{3} x \iff -\dfrac{x}{6}-5=\dfrac{2x}{3} }}[/tex]

Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

     [tex]\boldsymbol{\sf{ -\dfrac{x}{6}-5=\dfrac{2x}{3} \iff \ -x-30=4x}}[/tex]

The variable is moved to the left and the symbol is changed.

    [tex]\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}[/tex]

We move the constant to the right side and change the sign.

    [tex]\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}[/tex]

 [tex]\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}[/tex]

             [tex]\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}[/tex]

  [tex]\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-\dfrac{30}{5}=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}[/tex]

Answer:

  A, B, C

Step-by-step explanation:

You want to know the correct descriptors of the given graph.

The solution to a system of equations is the set of points that satisfy all of the equations at once. On a graph, it will be the set of points where the graphs of the equations intersect.

Here the two lines cross at one point, hence there is one solution.

The point where the lines cross is approximately (3, -0.5). That makes (3, -0.5) a reasonable estimate of the solution of the system.

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

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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If the circumference of ABDE is 30 cm, then the length of the line DE is 6 cm.

The answer to the query is

ABDE's perimeter is 30 cm.

AB length is 12 cm.

Let DE ne length be "x"

Since DE and AB are parallel, the alternate interior angles theorem states that

∠ABE = ∠DEB and ∠BAD = ∠ADE.

Since AD is the angle that bisects ∠A,

∠DAB = ∠EAD

BE is the angle bisector of B, therefore

∠EBD = ∠ABE.

∠EAD = ∠ADE and ∠EBD = ∠BED as a result.

If AE = ED and ED = DB, the triangles ADE and EDB are therefore isosceles. AE = DE = DB = x, then.

Given that ABDE's perimeter is 30 cm,

therefore 12 + 3x = 30,

By finding the x,

=> 3x = 30 -12

=> 3x = 18

=> x = 6 cm.

Consequently, DE has a length of 6 cm.

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Answer:

Step-by-step explanation:

-7-9=-16

Answer: The voting district that contributed the most to the test statistic is District B.

Step-by-step explanation:

How do you calculate the contribution of each voting district to the test statistic?

The contribution of each voting district to the test statistic is calculated by taking the difference between the observed and expected values for that district, squaring it, and then dividing it by the expected value. In this case, the contribution for District A is (58-46.80)^2/46.80 = 2.68, the contribution for District B is (22-32.40)^2/32.40 = 3.34, the contribution for District C is (12-18)^2/18 = 2.00, and the contribution for District D is (28-22.80)^2/22.80 = 1.19. Therefore, District B contributed the most to the test statistic.

The chi-square goodness-of-fit test compares observed and expected values to determine if they are significantly different from each other. The test statistic is calculated by summing the squared differences between the observed and expected values, divided by the expected values. The larger the difference between the observed and expected values, the larger the contribution to the test statistic. In this case, District B had the largest difference between the observed and expected values, therefore it had the greatest impact on the overall test statistic.

District B contributed the most to the test statistic because it had the highest value in the "Components" column. The formula for the chi-square goodness-of-fit test is (Observed - Expected)^2 / Expected, and the resulting value for District B is 3.34, which is the highest of the four districts. Therefore, District B had the biggest deviation from the hypothesized proportions.

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Answer: Voting district B contributed the most to the test statistic.

Step-by-step explanation:

How do you determine each voting district's contribution to the test statistic?

By subtracting the observed value from the predicted value for each voting district, square rooting the result, and then dividing the result by the expected value, the contribution of each voting district to the test statistic is determined. In this instance, the contributions for Districts A, B, C, and D are as follows:

District A's contribution is (58-46.80)²/46.80 = 2.68; District B's contribution is (22-32.40)²/32.40 = 3.34; District C's contribution is (12-18)²/18 = 2.00; and District D's contribution is (28-22.80)²/22.80 = 1.19. As a result, District B was most responsible for the test statistic.

In order to assess if actual and expected values differ significantly from one another, the chi-square goodness-of-fit test compares observed and expected values. The test statistic is determined by multiplying the expected values by the total of the squared discrepancies between the actual and predicted values. The contribution to the test statistic increases as the gap between observed and predicted values widens. In this instance, District B's largest disparity between actual and predicted values had the biggest effect on the test statistic as a whole.

Due to having the highest value in the "Components" column, District B had the greatest impact on the test statistic. (Observed - Expected)² / Expected is the formula for the chi-square goodness-of-fit test, and the result for District B, which is the highest of the four districts, is 3.34.

District B therefore, showed the greatest departure from the predicted proportions.

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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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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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