Round all answers to 4 decimal places unless otherwise noted.

1. 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) Describe the sampling distribution of the sample mean for the quantitative GRE scores for the 16 students. (Describe the shape, center, and spread)

b) 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?

c) What mean GRE score would mark the 45^th percentile in a sample of 16 students?

2) A random sample of size n is to be drawn from a population with? = 900 and? = 200. What size sample would be necessary in order to ensure a standard error of 10?

(Hint: Remember that

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x = Standard Error)