According to U.S. News&World; Report\'s publication America\'s Best Colleges, th

Question

According to U.S. News&World; Report's publication America's Best Colleges, the average cost to attend the University of Southern California (USC) after deducting grants based on need is $26,300. Assume the population standard deviation is S6,600. Suppose that a random sample of 60 USC students will be taken from this population a. What is the value of the standard error of the mean? (to nearest whole number) b. What is the probability that the sample mean will be more than 26,300? (to 2 decimals) c. What is the probability that the sample mean will be within $500 of the population mean? (to 4 decimals) d. How would the probability in part (c) change if the sample size were increased to 150? (to 4 decimals)

Explanation / Answer

n = 60 = 26300 = 6600

a. s = / n = 6600 / 60

= 852.

b. Since the value is equal to the population mean, probability

= 0.50.

c. X = 500

Z = 500 / (6600 / 60)

= 0.5868

Probability from table = 0.7213.

d. n = 150

Z = 500 / (6600 / 150)

= 0.9278

Probability from table = 0.8232.

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