7.40 Bank machine withdrawals An executive in an Australian savings bank decides to estimate the mean amount of money withdrawn in bank machine transactions. From past experience, she believes that $50 (Australian) is a reasonable guess for the standard deviation of the distribution of withdrawals. She would like her sample mean to be within

$10 of the population mean. Estimate the probability that this happens if she randomly samples 100 withdrawals.

(Hint: Find the standard deviation of the sample mean.

How many standard deviations does $10 equal?)