Question

The amount of time that a drive-through bank teller spends on a customer is a random

variable with a mean μ = 3.2 minutes and a standard deviation σ = 1.6 minutes. If a random

sample of 64 customers is observed, find the probability that their mean time at the teller’s

window is

a) at most 2.7 minutes;

Answer 1

$P(\bar X<2.7)=P(Z<\frac{2.7-3.2}{\frac{1.6}{\sqrt{64}}})=P(Z<-2.5)=1-P(Z<2.5)=$

$=1-0.9938=0.0032.$