The average credit card balance for college seniors is $2864. Use this figure as

Question

The average credit card balance for college seniors is $2864. Use this figure as the population mean and assume the population standard deviation is s=$775. Suppose that a random sample of 50 college seniors will be selected from the population.

- What is the value of the standard error of the mean ?

- What is the probability the sample mean will be greater than $3000 ?

- What is the probability the sample mean will be within $100 of the population mean ?

- How would this probability(answered in the previous question) change if the sample size were increased to 100 ?

Explanation / Answer

Given xbar=2864, s=775
n=50


- What is the value of the standard error of the mean ?
standard error of the mean = s/n =775/sqrt(50) =109.6016

- What is the probability the sample mean will be greater than $3000 ?

P(xbar > 3000) = P((xbar-mean)/(s/n) > (3000-2864)/109.6016)

=P(Z>1.24)

= 0.1075 (check standard normal table)

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