Assume the following 5 scores represent a sample: 2, 3, 5, 5, 6. Transform these scores into z-scores. Show all steps

Answers

Answer 1

The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

How to transform the scores?

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

[tex]\bar x = 4.2[/tex] --- mean

[tex]\sigma_x = 1.64[/tex] --- standard deviation

The z-score is then calculated using

[tex]z= \frac{x - \bar x}{\sigma}[/tex]

Where:

x = 2, 3, 5, 5, 6.

So, we have:

[tex]z_1= \frac{2 - 4.2}{1.64} = -1.34[/tex]

[tex]z_2= \frac{3 - 4.2}{1.64} = -0.73[/tex]

[tex]z_3= \frac{5 - 4.2}{1.64} = 0.48[/tex]

[tex]z_4= \frac{5 - 4.2}{1.64} = 0.48[/tex]

[tex]z_5= \frac{6 - 4.2}{1.64} = 1.10[/tex]

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

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Related Questions

The table below shows the number of correct answers that students gave on a recent 5-question quiz. Which of the following statements is true? Number Correct 1 2 3 4 5 3 46 9 8 Frequency​

Answers

The true statement about the number of correct answers is that the: A. median = mode.

How to calculate the mean?

Mathematically, the mean for the number of correct answers can be calculated by using the following formula:

Mean = [F(x)]/n

Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.

F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.

Mean = 105/30

Mean = 3.5.

For the median, we have:

The median for the number of correct answers is the average of the 15th and 16th number:

Median = (4 + 4)/2

Median = 8/2

Median = 4.

For the mode, we have:

The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.

Therefore, the true statement about the number of correct answers is that the median is equal to mode.

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Complete Question:

The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?

A. median = mode

B. mode > median

C. mode < mean

D. mean > median Reset Selection

PLEASE ANSWER ,in terms of the trigonometric ratios for BCD,what is the lenght of BD? insert text on the triangle in geogebrea to show the lenght of BD. take a screenshot of the triangle with the text,save it,and insert the image in the space below​

Answers

By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

How to calculate the length of BD?

In order to determine the length of side BD, we would apply the law of sine because both side BD and side BC represent the opposite side and hypotenuse of right-angled triangle BCD respectively.

Mathematically, the law of sine is given by this mathematical expression:

sin(θ) = Opp/Hyp

Where:

Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.

Substituting the parameters into the formula, we have;

sin(θ) = BD/BC

sin(74) = BD/9.41

Cross-multiplying, we have:

BD = 9.41 × sin(74)

BD = 9.41 × 0.9613

BD = 9.05 cm.

By applying the law of sine, the length of side BD is equal to 9.05 cm and the image of right-angled triangle BCD is shown in the image attached below.

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The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base

Answers

The circumference equal to 25 units

What is perimeter of square?

The perimeter of square is 4 times the side.

P= 4* side

The perimeter of the square,

4x = P

Now P is =  32 units then,

32 units = 4(x)

x = 8 inches

So,  the diameter of the cylinder formed by the rotation of 8 inches  

Now, the circumference of the base is

C = 2πr = πD

If r =8  inches

                           

C = π(8 units) = 8π units

C = 8(3.14) = 25.12 units

Hence, the circumference equal to 25 units

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2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3

Answers

3.

A = pi x r^2

48 = 3.141... x r^2

÷ by value of pi

15.278... = r^2

Square root the ans, to get r

Thus, R = 3.908..... So, radius is 3.9

2.

Circumference = pi x diameter

87. = 3.141... x d

÷ by value of pi

27.692............. = diameter

Radius is twice the diameter. So, divide diameter by 2 to find the radius.

27.692.....÷ 2 = 13.846...

Thus, radius is 13.8cm

Hope this helps!

Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $7$.

What is the sum of these three numbers?

Answers

Step-by-step explanation:

Smallest two digit number which is multiple of 7 = 14 (7*2)

Smallest three digit number which is multiple of 7 = 105 (7*15)

Smallest four digit number which is multiple of 7 = 1001 (7*143)

Sum = 14+105+1001 = 1120.

A freight train was supposed to travel 1300 miles in 50 hours. When the train had traveled 0.4 of this distance, it was delayed by 4 hours. What should the new speed of the train be to arrive on time?HELLPASAP

Answers

Answer:

The answer is 30 miles per hour

Step-by-step explanation:

1) From the question we can calculate the initial speed of the train

Initial speed = 1300 miles / 50 hours
                    =  26 miles / hour


2) Next, we can calculate the amount of distance already traveled:

Distance traveled = 1300 * 0.4

                              = 520 miles


3) Now let's calculate the amount of time it took to travel the 520 miles:
From point no. 1 we saw that it was traveling at the speed of 26 miles/ hour, so let's calculate the time elapsed.

Time elapsed = 520 miles / 26 hours

                       = 20 hours
But then again the text states the train was delayed by 4 hours, therefore the total time elapsed was 24 hours

4) Now to find the new speed required to arrive on time, we need to calculate how many hours and distance are left:

From point no. 2 we calculate the distance left
Distance left = 1300 - 520
                     = 780 miles

From point no. 3 we can calculate the amount of time left:
Time left = 50 - 24
               = 26 hours

Finally, we can find the new speed required to arrive on time:
New speed = 780 miles / 26 hours
                    = 30 miles / hour

The difference......

Answers

Answer:

[tex] log_{7}(3) [/tex]

Step-by-step explanation:

According to the

Law of logarithms,

[tex] log_{7}(18) \: - log_{7}(6) \\ \\ = \frac{ log_{7}(18) }{ log_{7}(6) } = log_{7}(3) [/tex]

How many different strings can be made by shuffling the letters in DISCRETEMATHS?

Answers

Answer:

I found 14 but their might be more!
hope that helps! :)

Step-by-step explanation:

Solve x 6x+2=2x-1 give your answer as a fraction in its simplest form

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{6x + 2 = 2x - 1}[/tex]

[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]

[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{4x + 2 = -1}[/tex]

[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]

[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{4x = -3}[/tex]

[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]

[tex]\huge\textbf{Simplify it!}[/tex]

[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]

[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Based only on the information given in the diagram which congruence theorems or postulate could be given as reasons why LMN and OPQ

Answers

The  congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.

What is congruence theorems?

Congruence theorems is one that explain that in a case whereby  three sides of two triangles are equal to another, we can say they are congruent to each other.

From the given figure, there are two angles as well as one non-included side which is seen to be a  congruent.

According to LA theorem , a triangle is congruent in a case whereby,  leg as well as  an acute angle of one right triangle of two right triangles are congruent to each other.

AAS theorem also explains that incase  two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.

Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.

CHECK THE FIQURE FOR THE COMNPLETE QUESTION

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What is the ratio of 12 blue marbles and 20 red marbles

Answers

Answer:

12:20

Step-by-step explanation:

i hope the answer will help you

Two student clubs were selling t-shirts and school notebooks to raise money for an upcoming school event. In the first few minutes, club A sold 3 t-shirts and 2 notebooks, and made $19. Club B sold 1 t-shirt and 1 notebook, for a total of $8. Use the given matrix equation to solve for the cost of t-shirts and notebooks that were sold. Explain the steps that you took to solve this problem.

A matrix with 2 rows and 2 columns, where row 1 is 3 and 2 and row 2 is 1 and 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 19 and row 2 is 8.

Answers

Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Variable x: Cost of a t-shirt.Variable y: Cost of a notebook.

Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:

3x + 2y = 19.x + y = 8 -> y = (8 - x).

Hence, replacing the second equation into the first:

3x + 2(8 - x) = 19

x = 3.

y = 8 - x = 8 - 3 = 5.

The cost of a t-shirt is of $3 and the cost of a notebook is of $5.

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The function f(x) is graphed. It represents a translation of the square root function g(x) = .



What equation represents the graph of f(x)?

f(x) =
f(x) =
f(x) = – 1
f(x) = + 1

Answers

The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]

How to determine the equation of f(x)?

The complete question is in the attached image

The parent square root function is:

[tex]g(x) = \sqrt x[/tex]

From the graph,

g(x) is shifted one unit right to get f(x)

This is represented as:

f(x) = g(x - 1)

So, we have:

[tex]f(x) = \sqrt {x - 1[/tex]

Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]

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A rectangle has length of 10 mm. • and breadth 7mm calculate its perimeter YW​

Answers

Answer:

34 mm

Step-by-step explanation:

P = 2 x (L + B) for a rectangle

P = 2 x (10 + 7) = 2 x 17 = 34

What is the domain indicated on the graph for each
portion of the piecewise function?
-2,
2x + 1,
--—-x,
f(x)=
Domain 1st piece
Domain 2nd piece
Domain 3rd piece

Answers

Step-by-step explanation:

try this option, all the details are in the attachment.

Giselle works as a carpenter and as a
blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.

Answers

Answer:

12 hours as a carpenter and 18 as a blacksmith.

Step-by-step explanation:

So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)

So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)

So we have the two equations:

c + b = 30

20c + 25b = 690

Now we can solve for c in terms of b and substitute that into the second equation:

Original equation:

c + b = 30

Subtract b from both sides

c = -b + 30

Original equation:

20c + 25b = 690

Substitute -b + 30 as c

20(-b + 30) + 25b = 690

Distribute the 20

-20b + 600 + 25b = 690

Simplify the equation

600 + 5b = 690

Subtract 600 from both sides

5b = 90

Divide both sides by 5

b = 18

Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation

Original equation

b + c = 30

Substitute 18 as b

18 + c = 30

Subtract 18 from both sides

12 = c

5. The function h(t) = 1 + 4t - 1.86t? models the height of a rock thrown upward on the planet Mars, where h(t) is height in meters and t is time in seconds. Use a graph to determine:

a. the maximum height the rock reaches
b. how long the rock will be above the surface

Answers

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

From the graph of the function h(t) = 1 + 4t - 1.86t²:

The maximum height the rock reaches 3.15 feet.

Time spent on air = 2.38 - (-0) = 2.38 seconds

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

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During the first year of life, a whale gains about 30 tons of weight what is the average weight gain per month?

Answers

Answer is 2.5 tons per month
Step by step
We know 30 tons gained over 12 months
(1 year)
Divide total weight by 12 months to get average weight gain per month
30/12 = 2.5 tons per month

match each equation to one of the graphs

Answers

Can you show us all the graphs

Answer:

I can only see one graph in that screenshot, so I graphed all of them. The one on your screenshot was B.

Use the table to work out the values of a, b,
C, and d.
X
-3
-2
-1
0
1
2
3
y = 5x

a
3x² + 3
- 19
-5
3
b
C
d

Answers

So to find the value of -3 do the following process:

Insert the -3 in the x’s in the equation on the top of the table

y= 5x -3x to the second power + 3

y= 5 (-3) -3(-3) to the second power + 3

Then continue to simplify the equation

y= -15 + 9 to the second power + 3

y= -15 + 84

y = 69

Y= 69 for the chart for -3

For b, c, and d insert the number in the x values and simplify like the previous equation.

If you are confused, feel free to ask questions. I hope this is effective and helps you in your studies.

The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.

Part B: Is the rate of change constant? Explain.

Part C: What was the hot air balloon's height at the time the descent began?

Part D: Write , as a linear function of
.

Answers

Using a linear function, we have that:

A. The rate of change is of -12 feet per second.

B. The rate of change is constant.

C. The initial height is of 1210 feet.

D. The linear function is: h(t) = -12t + 1210.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the table, when x changes by 5 seconds, the height decreases by 60 feet, hence the slope is given by:

m = -60/5 = -12 feet per second.

Hence the function is:

h(t) = -12t + b.

When t = 5, h(t) = 1150, hence we use this to find the initial height.

h(t) = -12t + b.

1150 = -12(5) + b.

b = 1210.

Hence the linear function is:

h(t) = -12t + 1210.

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DUE IN 3MINUTes
There is a strong positive linear correlation between rainfall and the number
of peaches a tree produces. Does this mean that more rainfall causes peach
trees to produce more fruit?
A. No. Any number of factors could also be affecting the number of
peaches produced.
B. No. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce less
fruit.
C. Yes. Since rainfall and number of peaches are positively
correlated, this means that more rainfall causes peach trees to
produce more fruit.
D. Yes. Since rainfall and number of peaches are linearly correlated,
this means that more rainfall causes peach trees to produce more
fruit.

Answers

Answer:

  A. No.

Step-by-step explanation:

The job of science is to explain relationships in the real world. Scientists do this by making observations, forming theories regarding relationships, and conducting experiments to test those theories.

An observation of correlation may result in a theory that one of the correlated phenomena causes another. The correlation, by itself, does not demonstrate causation. Any number of other factors could be involved.

Type the correct answer in each box. Use numerals instead of words. A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number. Teacher Doctor Athlete Boys 24 28 56 Girls 45 31 26 The marginal relative frequency of boys and girls who want to be a teacher is %. The joint relative frequency of girls who want to be an athlete is %. The conditional relative frequency of students that selected doctor, given that those students are boys is %.

Answers

The marginal relative frequency of boys and girls who want to be a teacher is 32 %. The joint relative frequency of girls who want to be an athlete is 25.4%. The conditional relative frequency of students that selected doctor, given that those students are boys is 51.85 %.

according to the question, the table given is
          Teacher - Doctor - Athete
boys
       24            28        56                     Total boys = 108

girls           45            31          26                  Total girls = 102

What is average?

Average of the values is the ratio of total sum of values to the number of values.


Conditions

1) for boys and girls whom opt for teacher,
   [tex]=\frac{69}{210} \\[/tex]

=     32%

2) for the girls who opt for athlete relative to girls,
   [tex]=\frac{26}{102}[/tex]
 =    25.4%

3) for the boys whom opt for doctors in boys
  =  [tex]\frac{28}{108}[/tex]
 =   25.9%

Thus, The required values of conditions 1,2,3 is  32%, 25.4%, 25.9% respectively

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Answer:

the answer is 33.       12.         and 26

Step-by-step explanation:

calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5

Answers

Answer:

13, -2

Step-by-step explanation:

How many significant figures are in the measurement 1.050 l? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d

Answers

There are 4 significant figures in the measurement 1.050 (Option d)

What are significant figures?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. We can determine how many significant figures in a given numbers by counting the number of digits that are significant to indicate the quantity or value of something.

How the measurement 1.050 has 4 significant figures?

Since the quantity 1.050 starts with 1, that is a non-zero digit, we start counting the significant figures starting from this digit. Thus, 1 is the first significant digit here. 0, 5, and 0 are the second, third, and fourth significant digit respectively.

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Answer:

option D

Step-by-step explanation:

just took the test

A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.

Answers

The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.

How to find the volume of a right rectangular prism?

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

V =  a × b × c unit³

The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]

                                                  = 310 inches²

The volume of the prism = 5 × 4 × 15

                                         = 300 in³

Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.


The complete question is:

A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?

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Find the largest rational number r for which 5r ≤ 33.

Answers

Answer:

33/5 or 6.6

Step-by-step explanation:

Well the most 5r can be is 33, since it has the underline under it, so it's less than or equal to.

So set 5r equal to 33

5r = 33

Divide both sides by 33

r = 33/5

You can leave it in this form or convert it to a decimal which is 6.6

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathsf{5r \leq 33}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{5r \leq 33}[/tex]

[tex]\huge\textbf{Divide \boxed{5} to both sides:}[/tex]

[tex]\mathsf{\dfrac{5r}{5}\leq \dfrac{33}{5}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{r \leq \dfrac{33}{5}}[/tex]

[tex]\mathsf{r \leq 6 \dfrac{3}{5}}[/tex]

[tex]\mathsf{r \leq 6.60}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{r \leq \dfrac{33}{5}}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\large\textsf{The graph will be labeled down below for you :)}\downarrow[/tex]

What are the medians for the height and weight distribution, respectively?

Answers

The median for height is: 167

The median for Weight is: 183

What is the Median of a Data Set?

The middle value or the average of the two middle value of an ordered data set is the median of the data.

Given the following data:

Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158

Arranged in an ordered form, we would have:

54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191

The middle value is 167. The median for height is: 167.

Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168

Arranged in an ordered form, we would have:

157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193

The middle value is 183. The median for weight is: 183.

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A
<
Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?

Answers

The test value and the p value for the probability are 10.5 and 0.0148.

How to illustrate the probability?

Based on the information, the observed and expected values will be:

Observed. Expected

75. 75

100. 120

90. 75

15. 30

The p value based on the test statistic from the distribution table will be 0.0148.

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The following graph shows a proportional relationship.
What is the constant of proportionality between y and x in the graph?

Answers

Answer:

[tex]k=2[/tex]

Step-by-step explanation:

The constant of proportionality is given as  [tex]k=\frac{y}{x}[/tex] .

Notice that when [tex]x=2[/tex] it follows that [tex]y=4[/tex].

Substitute [tex]x=2[/tex] and [tex]y=4[/tex] into the formula for the constant:

[tex]k=\frac{4}{2}=2[/tex] .

Therefore, the constant is equal to 2.

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