5. 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.) 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 147 on the quantitative portion
of the GRE?
b. Describe the sampling distribution of the sample mean for the quantitative GRE scores for the 16
students.
c. 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?
d. What is the probability that a random sample of 16 students has a mean score on the quantitative
portion of the GRE that is greater than 147?'