Question

e: W 3 Exercise (due Day 5] Saved The time it takes to give a man a shampoo and haircut is normally distributed with mean 22 minutes and standard deviation 3 minutes. Customers are scheduled every 30 minutes (a) What is the probability that a male customer will take longer than the allotted time? (Round your answer to 4 decimal places.) Probability (b) If three male customers are scheduled sequentially on the half hour, what is the probability that all three will be finished within their allotted half hour times? (Round your answer to 4 decimal places) Probability < Prey 11 of 15 !! Nond > e E 1 lp

Answer 1

Let X denote the time it taken by a man (in minutes). Then $X\sim N(22,3)$

a)

Required probability =

$\\P(X>30)=P(Z>\frac{30-22}{3})=P(Z>2.67)=1-P(Z<2.67)\\ \\ =1-0.9962=0.0038$

b)

P(finishing within the half-hour time) =

$\\P(X<30)=1-P(X>30)=1-0.0038=0.9962$

Required probability = $(0.9962)(0.9962)(0.9962)=0.9886$