Question
In: Statistics and Probability
(4 pts) The Graduate Record Examination (GRE) is a test required for admission to many U.S....
(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.
Solutions
Expert Solution
Solution :
Given that ,
mean = 
= 150
standard deviation = 
= 8.8
n = 16
Shape is approximately normal .
= 150 and
=
/ 
n = 8.8 /
16 = 8.8 / 4 = 2.2
P(
< 147) = P((
-
) /
< (147 - 150) / 2.2)
= P(z < -1.36)
Using standard normal table,
= 0.0869
Probability = 0.0869
Probability > 0.05
Outcome is not unusual .
orchestra answered 2 years agoRelated Solutions
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