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To check the Ace company's claim that the total of their 2,500 accounts receivable was $1,175,000 and that the standard deviation of the individual accounts was $ 200 the external auditor took a sample of 25 accounts which totalled $9,475.

a) If the company's report is correct, what is the probability that the average balance of an account in the sample is $394 or less?

b) If the total of the accounts receivable is only $1,000,000 (but the standard deviation was correct), what is the probability the total of the sample would be less than $9,475?

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