Exercise 6.89 describes scores on the Critical Reading portion of the Scholastic Aptitude Test (SAT) for college-bound students in the class of 2010. Critical Reading scores are approximately normally distributed with mean μ = 501 and standard deviation σ = 112.

(a) For each sample size below, use a normal distribution to find the percentage of sample means that will be greater than or equal to 525. Assume the samples are random samples.

i. n = 1

ii. n = 10

iii. n = 100

iv. n = 1000

(b) Considering your answers from part (a), discuss the effect of the sample size on the likelihood of a sample mean being as far from the population mean as x̅ = 525 is from μ = 501.