The time that customers take to complete their transactions at an ATM is a rando

Question

The time that customers take to complete their transactions at an ATM is a random variable with mean 2 minutes and standard deviation of .6 minute. a. What is the probability that the average ATM-transaction time for a random sample of 50 customers will be between 1.8 and 2.25 minutes? b. What is the probability that the total ATM-transaction time for a random sample of 36 customers is less than one hour? c. There is a 90% probability that the average ATM-transaction time for a random sample of 50 customers is at least how many minutes?

Explanation / Answer

c) The probability mentioned is for the right tail, as it mentions "atleast" how many minutes
P(X > x) = 0.9, P(X < x) = 0.1
For p = 0.1, z = 1.2816
z = (x - µ)/(/sqrt(n)) = (x-2)/(0.6/sqrt(50)) = 1.2816
x = 2.1087

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