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
egoroff_w [7]
3 years ago
10

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:
elena-14-01-66 [18.8K]3 years ago
4 0

Answer:

Kindly check explanation

Step-by-step explanation:

Given The following :

Assume score is normally distributed with;

Mean (m) = 1049

Standard deviation (sd) = 189

Numbw rof observations (n) = 16

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

Zscore = (x - m) / sd

X = 1100

Zscore = (1100 - 1049) / 189

Zscore = 51 / 189 = 0.27

From z-table ; 0.27 correspond to 0.6064

P(X > 1100) = 1 - P(X < 1100) = 1 - 0.6064 = 0.3936

2) sample mean will be equal to population mean = 1049

Sample Standard deviation : (population standard deviation / sqrt (n))

= 189 / sqrt(16) = 189/4 = 47.25

Shape of distribution is approximately normal

3)

P(Z < 1100)

X = 1100

Zscore = (x - m) / standard error

Standard Error = population standard deviation / sqrt (n)

= 189 / 4 = 47.25

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

From z-table :

P(Z < 1100) = 0.8599

4)

D.)

P(Z > 1100)

X = 1100

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

From z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.140

E)

With a sample size of 64

Standard Error becomes:

189 / sqrt(64) = 189/ 8 = 23.63

Zscore = (1100 - 1049) / 23.63

Zscore = 51 / 23.63 = 2.16

P(Z > 2.16) = 1 - P(Z < 2.16) = 1 - 0.9846 = 0.0154

Probability is less due to increase in sample size

You might be interested in
The mean height of plants is 18 inches. The height of seven plants are 12 inches, 13 inches, 15 inches, 15 inches, 17 inches, 23
ahrayia [7]

Answer:

25 inches

Step-by-step explanation:

i first started with 18×8=144 then i did 144-119 and got 25.

3 0
3 years ago
A falcon can fly 322 km/h how many meters per hour can the falcon fly
Tju [1.3M]
322 km/h = 322000 meters/h

Hope This Helps :)
8 0
3 years ago
Why there must be at least two lines on any given plane
ratelena [41]
Although theoretically there are infinite lines in space and in a plane, too, at least three non collinear points are necessary to define a plane. Two intersecting lines will therefore be necessary to define it (two points create a line); these intersecting lines are the ones to help define coordinates (x,y).
7 0
3 years ago
What is the combined length of 5/8
Kipish [7]
5/8 + 5/8 + 5/8 = 15/8 = 1 7/8 inches.
7 0
3 years ago
Brainiest!!! please I need help<br>​
iVinArrow [24]

Answer:

we i now it its

Step-by-step explanation:

1 distrubutiv propety

2'community of addition

3 addition on unlike term

4 0
2 years ago
Other questions:
  • How do you wright 19,266,420 using words
    13·2 answers
  • a committee has eleven members. there are 3 members that currently serve as the boards chairman, ranking members, and treasurer.
    14·1 answer
  • How do you factor 6x^3 +5x^2-4x
    7·1 answer
  • PLEASE HELP!!
    8·2 answers
  • What expression is equivalent to (x+7)+3y
    11·1 answer
  • Pls help ASAP I need help on this problem
    7·1 answer
  • Help I’m doing a test.... what is 3(2x-9) =
    8·2 answers
  • What is the answer for x?
    10·1 answer
  • Graph the following log function and describe the key characteristics (Domain, range, asymptote, shifts, intercepts): f(x) = log
    10·1 answer
  • Given the two half-reactions, what must be done in the next step before the reaction can be balanced? First: upper A u superscri
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!