Question

**1.** (6 pts) The Graduate Record Examination
(GRE) is a test required for admission to many U.S. graduate
schools. Students' scores on the quantitative portion of the GRE
follow a normal distribution with mean 150 and standard deviation
8.8. In addition to other qualifications, a score of at least 160
is required for admission to a particular graduate school.

- What proportion of combined scores can be expected to be over 160?

- What proportion of combined GRE scores can be expected to be between 155 and 160?

- What is the probability that a randomly selected student will score less than 150 points?

- Historically, Department of History at NYU has admitted students whose quantitative GRE score is at least at the 61st percentile. What is the lowest GRE score of the students they admit?

- Determine the range of scores that make up the middle 95% of scores.

**2.**(4 pts) The Graduate Record Examination (GRE)
is a test required for admission to many U.S. graduate schools.
Students' scores on the quantitative portion of the GRE follow a
normal distribution with mean 150 and standard deviation 8.8. In
addition to other qualifications, a score of at least 160 is
required for admission to a particular graduate school.

**Suppose n = 16 randomly selected students take the GRE
on the same day.**

- Describe the sampling distribution of the sample mean for the quantitative GRE Scores for the 16 students. (give the shape, mean, and SD)

- What is the probability that a random sample of 16 students has a mean score on the quantitative portion of the GRE that is less than 147? Would this be an unusual outcome.

**3.** (4 pts) According to a recent article, 32%
of drivers had driven drowsy in the past month. (Source:
Thenationshealth.aphapublications.org/content/41/10/E52.fuII)

Suppose law enforcement officials are planning a survey of 1000 drivers to determine what proportion are driving drowsy.

- Is whether a driver has driven drowsy in the past month qualitative or quantitative?

- Would it be unusual if, in a random sample of 1000 drivers, 35% or more were driving drowsy in the last month? Include justifications for full credit.

- What is the minimum number of drivers that must be sampled to
be sure that the shape is approximately normal?
*Hint – use the formula*

**4.** (6 pts) The Graduate Management Admission
Test (GMAT) is a test required for admission into many masters of
business administration (MBA) programs. Suppose a random sample of
8 students took the test, and their scores are given below.

699, 560, 414, 570, 521, 663, 727, 413

- Find a point estimate of the population mean.

- Construct a 95% confidence interval for the true mean score for the population.

- Interpret the interval you constructed above.

- How many students should be surveyed to estimate the mean score
within 25 points with 95% confidence?
*Hint – use the formula*

Answer #1

1)

P(x> 160)

= P(z > (160 - 150)/8.8)

= P(z > 1.1364)

= 0.1279

b)

P(155 < x < 160)

= P((155 - 150)/8.8 < z < ( 160 -150)/8.8)

= P(0.5682 < z < 1.1364)

= 0.1571

c)

P(x< 150)

= P(z < (150 - 150)/8.8)

= P(z < 0)

= 0.5

d)

z value at 61 percentile = 0.2793

z = (x -mean)/s

0.2793 = ( x - 150)/8.8

x = 152.4580

e)

z value at 95% 1.96

CI = mean +/- z *s

= 150 +/- 1.96 * 8.8

= (132.7520,167.2480)

Lower Bound = 132.7520

Upper bound = 167.2480

The Graduate Record Examination (GRE) is a test required for
admission to many U.S. graduate schools. Students’ scores on the
quantitative portion of the GRE follow a normal distribution with
mean 150 and standard deviation 8.8. (Source:www.ets.org). A
graduate school requires that students score above 160 to be
admitted
6. What is the percentile rank of a student who earns a
quantitative GRE score of 142?
7. Historically, Depart of History at NYU has admitted students
whose quantitative GRE score...

PLEASE TYPE DO NOT WRITE THANK YOU!
The Graduate Record Examination (GRE) is a test required for
admission to many US graduate schools. Students’ scores on the
quantitative portion of the GRE follow a normal distribution with a
mean of 150 and a standard deviation of 8.8. In addition to other
qualifications, a score of at least 152 is required for admission
to a particular graduate school.
a )Determine the 80thpercentile of GRE scores.
b) Determine the GRE scores that...

The Graduate Record Examination (GRE) is a test require for
admission to many U.S graduate schools. Students' scored on the
quantitative portion of the GRE follow a normal distribution with
mean 150 and standard deviation 8.8. A graduate school requires
that sudents score above 160 to be admitted
1. Determine the combined GRE scores that make up the middle 95%
of all scores?
Use the standard normal distribution to determine the
following:
2.) 68% of the scores lie between what...

The Graduate Record Examination (GRE) is a standardized test
commonly taken by graduate school applicants in the United States.
The total score is comprised of three compo- nents: Quantitative
Reasoning, Verbal Reasoning, and Analytical Writing. The first two
components are scored from 130 - 170. The mean score for Verbal
Reasoning section for all test takers was 151 with a standard
deviation of 7, and the mean score for the Quantitative Reasoning
was 153 with a standard deviation of 7.67....

Amanda took the Graduate Record Examination (GRE), and scored
160 in verbal reasoning and 157 in quantitative reasoning. The mean
score for verbal reasoning was 151 with a standard deviation of 7,
compared with mean µ = 153 and σ = 7.67 for quantitative reasoning.
Assume that both distributions are normal.
(a) What were Amanda’s Z-scores on these exam sections? Mark
these scores on a standard normal distribution curve.
(b) Which section did she do better on, relative to other...

The Graduate Management Admission Test (GMAT) is a test required
for admission into many masters of business administration (MBA)
programs. GMAT scores are normally distributed. Suppose a random
sample of 8 students took the test and their scores are given
below:
699 560 414 570 521 663 727 413
Construct a 90% confidence interval for the true mean score for
the population and interpret.

According to a recent article, 32% of drivers had driven drowsy
in the past month. (Source:
Thenationshealth.aphapublications.org/content/41/10/E52.fuII)
Suppose law enforcement officials are planning a survey of 1000
drivers to determine what proportion are driving drowsy.
A. Is whether a driver has driven drowsy in the past month
qualitative or quantitative?
B. Would it be unusual if, in a random sample of 1000 drivers,
35% or more were driving drowsy in the last month? Include
justifications for full credit.
C. What...

Answer only questions 1,2,3,4
The Graduate Management Admission Test
(GMAT) is a test required for admission into many masters of
business administration (MBA) programs. Total scores on the GMAT
are normally distributed and historically have a population
standard deviation of 113. The Graduate Management Admission
Council (GMAC), who administers the test, claims that the mean
total score is 529.
Suppose a random sample of 8 students
took the test, and their scores are given below.
699
560
514
570
521...

Most graduate schools of business require applicants for
admission to take the Graduate Management Admission Council’s GMAT
examination. Scores on the GMAT are roughly normally distributed
with a mean of 527 and a standard deviation of 112.
If a prestigious business school will only take those students
who score in the top 5%, what score would you need to have to be
accepted?

1. The Graduate Record Exam (GRE verbal test) has scores that
are normally distributed with a mean of 532 and a standard
deviation of 128. If one test taker is chosen at random, what is
the probability that the person's GRE verbal score is above 500?
Use Table 8.1 and leave answer in decimal form.
2. The Graduate Record Exam (GRE verbal test) has scores that
are normally distributed with a mean of 532 and a standard
deviation of 128....

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