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
Arlecino [84]
3 years ago
14

The combined (verbal + quantitative reasoning) score on the GRE (Graduate Record Exam) is normally distributed with mean 1049 an

d standard deviation 189. Suppose n = 16 randomly selected students take the GRE on the same day.
a. What is the probability that one randomly selected student scores above 1100 on the GRE?
b. Describe the sampling distribution of the sample mean for the 16 students (description should include mean, standard deviation and shape).
c. What is the probability that a random sample of 16 students has a mean GRE score that is less than 1100?
d. What is the probability that a random sample of 16 students has a mean score that is more than 1100?
e. If the sample size in (d) above was increased to 64, what affect would it have on the probability (more, less, the same, can't tell) and why?
Mathematics
1 answer:
mash [69]3 years ago
3 0

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Normal distribution :

Mean (m) = 1049

Standard deviation (sd) = 189

Number of samples (n) = 16

A) What is the probability that one randomly selected student scores above 1100 on the GRE?

Obtain the z score

Zscore = (x - m) / sd

Zscore = (1100 - 1049) / 189

Zscore = 51 / 189 = 0.2698412 = 0.27

Using the z-table

P(X > 100) = 1 - P(X < 100) = 1 - 0.6064 = 0.3936

B) The sample mean = population mean

Hence sample mean = 1049

The sample standard deviation = standard error

Standard Error (SE) = sd / sqrt(n)

SE = 189/4 = 47.25

Hence shape = normal, standard deviation = 47.25, mean = 1049

C.) P(X < 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X < 1100) = 0.8599

D.) P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.1401

E) if n = 64

SE = 189 / sqrt(64) = 189 / 8 = 23.625

P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 23.625

Zscore = 51 / 47.25 = 2.1587301 = 2.16

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.9846) = 0.0154

The probability decreases as the same distribution hinges towards a Boal distribution with increasing sample size.

You might be interested in
The spanish club has 78 members, 42 girls and 36 boys whats the ratio
Makovka662 [10]
The ratio fo boys to girls is 12:16
5 0
3 years ago
Read 2 more answers
10. 2x + 7y = 1<br> 2x - 4y = 12<br> Solve for y
adoni [48]

Answer:

The solution for y = -1.

Step-by-step explanation:

Given:

2x\ +\ 7y\ =\ 1    ....(1)

2x\ -\ 4y\ =\ 12  ....(2)

So, to solve for y, first we solve for x in equation (2):

2x-4y=12

⇒2x=12+4y

Dividing both sides by 2,

⇒x=6+2y            

Now, substituting the value of x  in equation (1):

2x+7y=1

⇒2(6+2y)+7y=1

⇒12+4y+7y=1

⇒12+11y=1

⇒11y=1-12

⇒11y=-11

Dividing both sides by 11,

⇒y=-1

Therefore, the solution for y = -1.

7 0
3 years ago
HELP PLEASE!!! The length of a rectangle is shown below:
Kamila [148]

Answer:

B

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
The angle shown is in standard position. Select the possible measures of the angle. –450° –360° –270° –90° 90° 270° 360° 450° On
erma4kov [3.2K]

Answer:

-450

-90

270

Step-by-step explanation: Just did it on edgen-uity

4 0
3 years ago
Read 2 more answers
What does AB congruent symbol CD mean? AB and CD here have lines over them How is it different than AB=CD?
masha68 [24]

Answer:

Suppose that we have two line segments, AB and CD. We know that they have the same length.

I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Which is the simplified form of the expression
    15·1 answer
  • How to solve for x for a parallelogram
    5·2 answers
  • Their are 40 coin of dimes and quaters and they make $4.90 how much of each coin is their
    8·1 answer
  • Question down below in the picture :DD
    8·1 answer
  • Find f(4) for f(x) = 4x + 3.<br><br> f(4) =
    5·1 answer
  • Place these numbers in order from least to greatest:<br><br> 16/5 -3 6 3.1 -2.5 1/4 -3/4 -3/8
    9·1 answer
  • Select all the equations that have 9 as a solution.
    12·2 answers
  • PLZ
    7·1 answer
  • If the hypotenuse is 20 and one of the legs is 12, what is the length of the missing leg?
    13·2 answers
  • To the nearest thousandth, what is the decimal form of 9/14​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!