1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vlad [161]
3 years ago
15

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. Teh mean is 73, wit

h a standard deviation of 7. The teacher wishes to give A's to the top 5.5% of the students and F's to the bottom 5.5%. A grade of B is given to the next 19.7%, with D's given similarly. All other students get C's. Find the bottom cutoff for a grade of A.
The bottom for an A is _____. Round to the nearest whole number as needed.
Mathematics
1 answer:
zavuch27 [327]3 years ago
8 0

Answer:

The bottom for an A is 75. Round to the nearest whole number as needed.

Step-by-step explanation:

1) Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the scores on this case, and for this case we know the distribution for X is given by:

X \sim N(\mu=73,\sigma=7)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

2) The bottom for an A is _____. Round to the nearest whole number as needed.

And we want the top 5.5% of the scores, so we need a value a such that:

P(X>a)=0.055 or P(X

We need on the right tail of the distribution a value a that gives to us 94.5% of the area below and 5.5% of the area above. Both conditions are equivalent.

Let's use the condition P(X, the best way to solve this problem is using the z score with the following formula:

z=\frac{x-\mu}{\sigma}

So we need a value from the normal standard distribution that accumulates 0.945 of the area on the left and 0.055 on the right. This value on this case is 1.598 and we can founded with the following code in excel:

"=NORM.INV(0.945,0,1)"

If we apply the z score formula to our case we have this:

P(X

So then based on the equalities we have this:

\frac{a-73}{7}=1.598

And if we solve for a we got:

a=(7*1.598) +73=84.186

So then we need a score of 84.186 rounded to the nearest whole number 75 or higher in order to get an A

You might be interested in
HELPPPPPPPP I am taking it now
Elena-2011 [213]

Answer:

I'm pretty sure the answer is -a²b and 5a²b

Step-by-step explanation:

8 0
3 years ago
Find the product of 2/5 with the quotient of 7/3 and 4/5
marissa [1.9K]

Answer:

7/6

Step-by-step explanation:

7/3÷4/5

7/3×5/4

35/12

Now the multiplication

2/5×35/12

70/60

7/6

6 0
2 years ago
A 29<br> B 58<br> C 13.5<br> D 14.5
matrenka [14]
The answer is d actually I don’t know
8 0
3 years ago
Which describes how to find the solution 5k &gt;22
inysia [295]

Answer:

<h2>k > 4.4</h2>

Step-by-step explanation:

5k>22\qquad\text{divide both sides by 5}\\\\\dfrac{5k}{5}>\dfrac{22}{5}\\\\k>4\dfrac{2}{5}\to k>4.4\to k\in(4.4,\ \infty)

8 0
3 years ago
Given y varies inversely as x, and y = 5 when x = 9. *Write the inverse function
Ivahew [28]

Answer:

y = 45/x

Step-by-step explanation:

Here, we want to write an inverse relationship

for an inverse relationship, the product of both variables will be equal to the constant term

Let us have the constant term as k

Thus, we have it that;

xy = k

9 * 5 = k

k = 45

So the inverse function is;

xy = 45

or y = 45/x

if y is a function of x, we can have it as;

f(x) = 45/x

4 0
3 years ago
Other questions:
  • the city of Boston has about 614594 residents to the nearest ten thousand what is the population of Boston
    11·1 answer
  • On a number​ line, A is at negative 7 and B is at 3. What is the coordinate of​ C, which is two fifths of the way from A to​ B?
    10·1 answer
  • What is 15 = -y + 10
    15·2 answers
  • for every 4 miles vanessa jogged, cody jogged 3 miles. if vanessa jogged 1 miles, how far would cody have jogged
    12·2 answers
  • I will give 98 points and brainliest for who ever gets these right!! (1.)what is the value of 3+y÷4,when y= 16? (2.) evaluate th
    9·2 answers
  • Which of these divisibility rules can be applied to determine if 315 is a prime or composite number?
    5·1 answer
  • Select THREE expressions equivalent to - 81x + 27.
    6·1 answer
  • What is the value of x in the equation 5x - 3x + 4(1-4x) = 32?
    14·2 answers
  • A thearte ticket costs £63 plus a booking fee of 3%<br> what is the total price of the ticket
    13·2 answers
  • In 3 hours, Fast Eddy performed 21 663 loops with his yo-yo. How manyloops could he do in 8 hours at this rate?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!