Question

A local bank reported to the federal government that its 5,246 saving accounts have a mean of $1,000 and standard deviation of $240. government auditors have asked to randomly sample 64 of the bank's accounts to assess the reliability of the mean balance reported by the bank. if the bank information is correct, what is the probability that the sample mean balance would be less than $928?

Answer 1

Find the Z score and use a Z Score Deviation graph. For $928 in a bank account, with mean balance $1000, and SD of $240, the Z-score is [(928-100)/240] = [-0.3] = 0.3. Interpreting the graph, 0.618 or 62% probability that the balance is less than $928.