Question

At Acme Bank the total amount of money that customers withdraw from an automatic teller machine (ATM) each day is believed to be normally distributed with a mean of $8600 and a variance of 6250000. i) At the beginning of weekday (M-F), the Acme Bank puts $10000 into the automatic teller machine. What is the probability that the ATM becomes empty before the end of the day. ii) How much should the Acme Bank put in the ATM each day in order to satisfy daily demand 99% of the time. iii) On a Saturday if customers withdraw from the (ATM) becomes below average, what is the probability that it will be below $6000? iv) If you select random samples of 25 from Acme Bank ATM users, what percentage of the sample means withdraws would be more than 10,000 from the ATM? v) In a random sample of size 25, what is the probability that sample mean withdraw exceeds 12000?

Answer 1

Given that withdrawal from an automatic teller machine (ATM) each day is believed to be normally distributed with a mean of and a variance of .

i) The probability that the ATM becomes empty before the end of the day is

ii) Let be the minimum amount the bank should put in the ATM each day to satisfy 99% of the demands, then

iii) The probability,

The conditional probability,

iv) The distribution of sample mean is .

The probability,

The required percentage is 0.26%.

v) As in part (iv),