A psychology professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the top 9% and above the bottom 56% C: Scores below the top 44% and above the bottom 20% D: Scores below the top 80% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answers

Answer 1

Answer:

You get a D if you have a grade between 66 and 72.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4.

This means that [tex]\mu = 79.3, \sigma = 8.4[/tex]

D: Scores below the top 80% and above the bottom 6%

So between the 6th and the 20th percentile.

6th percentile:

X when Z has a pvalue of 0.06. So X when Z = -1.555.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.555 = \frac{X - 79.3}{8.4}[/tex]

[tex]X - 79.3 = -1.555*8.4[/tex]

[tex]X = 66.2[/tex]

Rounds to 66

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X - 79.3}{8.4}[/tex]

[tex]X - 79.3 = -0.84*8.4[/tex]

[tex]X = 72.2[/tex]

Rounds to 72

You get a D if you have a grade between 66 and 72.


Related Questions

Make a equation for the scatter plot line

Answers

Answer:

y = -7.2x + 540

Step-by-step explanation:

to find the slope I used the x-and-y intercepts: (0, 540) and (75, 0)

slope = 540/-75 or -7.2

HELP HELP
Tommy rides in a motorboat against a river current for 25 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 10 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 12 km/h.

Answers

The speed of current is [tex]\rm 2 \:km/h[/tex].

What is the relation between distance,speed and time?

The relationship between distance, time and speed can be presented as:

[tex]\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end[/tex]

Calculations:

Given:

[tex]\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end[/tex]  

 

Let the speed of the current be [tex]\rm x[/tex]

 

The speed of the boat traveling against the current is [tex]{(12 -\rm x) km/h}[/tex]

 

Time spent on motorboat is 10 hours less than time spent on raft.

Therefore:

[tex]\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10[/tex]


The equation obtained will be:

[tex]\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10[/tex]

 

Multiplying both sides of the equation by [tex]\rm x(12 - x )[/tex]

[tex]\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end[/tex]

Dividing the equation by 10

[tex]\rm x^2 - 17x + 30 = 0[/tex]

On factoring the equation,

[tex]\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)[/tex]

The values of x is 2 and 15.

Since speed of current i.e  [tex](12 -\rm x)km/h[/tex] cannot be negative, [tex]\rm x = 2[/tex] is the only acceptable value.

 Therefore the speed of current is 2 km/h.

Learn more about the topic here:

https://brainly.com/question/2292310

Write an expression for the sequence of operations described below.
10 plus the quotient of 8 and u
Do not simplify any part of the expression.

Answers

Answer:

[tex]10 + \frac{8}{u}[/tex]

Step-by-step explanation:

Given

10 [tex]plus[/tex] the  [tex]quotient[/tex]of 8 and u

Required

Represent as a mathematical expression

Square out the operators

10 [[tex]plus[/tex]] the  [[tex]quotient[/tex]] of 8 and u

[tex]plus => +[/tex]

[tex]quotient => /[/tex]

Replace the operators with their signs

[tex]10 + \frac{8}{u}[/tex]

Help please someone A, B, or C ?

Answers

Answer:

it got to be b 2:2

please help i will give brainliest

Answers

Answer : Line 1


Explanation: at the 1 hour mark on the x axis the line that goes through the 120 mark on the y axis is line 1

Is this right? Please help

Answers

Answer: I believe that is correct! good jobbb

Step-by-step explanation:

the tax on a purchase of $20 is $2.80. How much tax will there be on a purchase of $45.50?

Answers

Answer:

$6.37

Step-by-step explanation:

You divide 2.80 by 20 to find the percentage of tax then you simply multiply your percentange by the cost. In this problem the tax was 14% or .14, so you multiply .14 by 45.50 to find the amount of tax on the purchase

Don operates a small craft store in which he sells other peoples crafts. He takes a 45% commission from the sales of all crafts. If he earns $958.00 Commission last week, how much did he sell?

Answers

Answer:

2,128

Step-by-step explanation:

958=45/100 x

958= 0.45* x

x=958/0.45

x=2,128 approximately

Hope that helps!

Can someone please help!!!

Answers

Answer:

its the 3rd one

Step-by-step explanation:

1
Cindy has a 4-shelf bookcase in which she wants to place baskets. Each basket takes up of one shelf as shown
4
Cindy wants to place as many baskets on the shelves as possible. How many baskets can Cindy place on the 4 shelves?
Previous

Answers

Answer:

obviously 16 books....

You cannot use critical numbers and test intervals to solve quadratic and
rational inequalities.
True
False

Answers

Answer:

False

Step-by-step explanation:

You can use test intervals and critical numbers to solve quadratic and rational inequalities.

Factor the algebraic expression.
12a+9

Answers

3(4a+3)

Hope this helps!! :)

Can someone please help me answer this is a test and I need to hurry

Answers

Answer:

27

Step-by-step explanation:

The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3 what is the common ratio in this sequence

Answers

Answer:

The common ratio in this sequence is 6:2 or 4:3

Step-by-step explanation:

hopes this heklps

PLS HELPPP
What value of x would make the following relation a function?
{(-3,-2),(2,3),(3,2),(x,2)}

A. -3
B. -2
C. 2
D. 3

Answers

A........................................

Which equation represents the function f(x) = (1.6)x after it has been translated 5 units up and 9 units to the right?

Answers

g(x) = (1.6)x − 9 + 5

Answer:

It's C. g(x) = (1.6)x − 9 + 5

Step-by-step explanation: hope it helps ^w^

What percent of $80 is $20

Answers

Answer: $20$20​ is $25\%$25%​ of $80$80​.

Step-by-step explanation:

25

Which of the following World Record times from Track and Field is least
precise?
A. 47.6 seconds (400 m -Women)
B. 43.18 seconds (400 m - Men)
C. 21.34 seconds (200 m-Women)
D. 9.79 seconds (100 m - Men)

Answers

Answer:

THE ANSWER SHOULD BE D OR B

Step-by-step explanation:

I DON'T KNOW

what is the square root of -20

Answers

Answer:

4.47213595

Simplify in the tenths place and get 4.47

Step-by-step explanation:

(9x10^10) - (4x10^10)

Answers

Answer: 50000000000 is your answer.

Step-by-step explanation:

g Suppose the population 10-year cumulative incidence of prostate cancer among 70-year old men is 0.06. Further, suppose 260 men without prostate cancer, aged 50 years were randomly sampled and 13 of them developed prostate cancer within 10 years. Is there evidence at the 0.05 significance level to conclude that the cumulative incidence of prostate cancer among 50-year old men differs from that of 70-year old men

Answers

Answer:

There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

Step-by-step explanation:

The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06

The number of 50 year old men in the sample, n = 260 men

The number of the sampled men that developed prostrate cancer = 13 men

The significance level, α = 0.05

Let the null hypothesis, H₀: [tex]\hat{p}[/tex] = p

The alternative hypothesis, Hₐ: [tex]\hat{p}[/tex] ≠ p

The standard score, [tex]z_{\alpha /2}[/tex] = 1.96

The test statistic, 'z', is given as follows;

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]

[tex]\hat{p}[/tex] = 13/260 = 0.05

q = 1 - p = 1 - 0.06 = 0.94

[tex]Therefore, \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68[/tex]

From the z-table, we find the p-value as follows;

P(z ≈ -0.68) = 0.24825

Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

(x2 – 3x + 2)/(4x - 16)

Answers

Answer:

Pretty sure it's x^2−3x+2/4x-16  

Step-by-step explanation:

Given that A and I are the centers of the congruent circles shown below, compare the quantity in column A with the quantity in column B. Choose the best answer. The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

Answers

Answer: The two quantities are equal

Step-by-step explanation:

Edge2021

C. The two quantities are equal

Step-by-step explanation:

Edge 2020 2021

PLEASE HELP MEE it’s urgent

Answers

Answer:

positive9/50

Step-by-step explanation:

9/50

Answer:

the answer is 9/50 (fraction).

Step-by-step explanation:

hope this helped!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Suppose two angles in a coordinate plane, one measuring 80° and the other measuring 160°, were both rotated 180° about the origin and then translated 40 units down. Which of these would be a measure of
one of the resulting angles? Select all that apply.
160°
340°
80°
40°
120°
260°

Answers

Answer:120 and 160

Step-by-step explanation:

i did it

80° and 160° could be a measure of one of the resulting angles.

What are angles?

Two rays intersect to form a angle. The point of intersection is called the vertex point.

Given is that  two angles in a coordinate plane, one measuring 80° and the other measuring 160°, were both rotated 180° about the origin and then translated 40 units down.

There is no effect of rotation and translations on the angles. Hence, we can say that 80° and 160° could be a measure of one of the resulting angles.

Therefore, 80° and 160° could be a measure of one of the resulting angles.

To solve more questions on angles visit the link below-

brainly.com/question/1041084

#SPJ6

pls answer this-.....​

Answers

AnswerS:

Let A be the surface area, b the base, h the height;

h₁=8.4 cm

h₂=7.8 cm

b= 9 cm

A= 3(1/2bh₁)+1/2 bh₂

A=3(1/2(9)(8.4))+1/2 (9)(7.8)

A= 148.5 cm³

Answer:

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as:  

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface are

what shape can be formed from the following net?​

Answers

Answer:

A Triangular Prism    

Hope that helps!

Step-by-step explanation:

Answer: Triage

Step-by-step explanation:

The matrix is used to solve a problem. Which of the following would be a solution to the problem?

Answers

Answer:

(1,5)

Step-by-step explanation:

Hope this is right.

Answer:

It's (1,0)

Step-by-step explanation:

I got it right on the quiz

The factors of a polynomial are (x + 3x - 2)(x+ 7) The polynomial has been graphed. How do the zeros relate to the factors?

A. The zero is the sum of the numbers inside the parenthesis

B. There is no relationship between the factors and the zeros.

C. The number inside each parenthesis are the zeros of the equation.

D. If you set each factor equal to 0 and solved you would get the zeros.​

Answers

Answer:

its C I am pretty sure about it

Answer:

D: If you set each factor equal to 0 and solved you would get the zeros.

Step-by-step explanation:

Completed it on PL also because 0 should be base

Use each number in the box once to complete the division
5÷6,206

Answers

Answer:

i believe it is 1,241.2

Step-by-step explanation:

well you use long division.

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