Please solve and explain: The time it takes to give a man a shampoo and haircut
ID: 3049329 • Letter: P
Question
Please solve and explain:
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.) ProbabilityExplanation / Answer
a) P(X > 30) = P((X - mean)/sd > (30 - mean)/sd)
= P(Z > (30 - 22)/3)
= P(Z > 2.67)
= 1 - P(Z < 2.67)
= 1 - 0.9962 = 0.0038
b) P((X - mean)/sd < (30 - mean)/sd)
= P(Z < (30 - 22)/3)
= P(Z < 2.67)
= 0.9962
P(X = 3) = 3C3 * (0.9962)^3 * (1 - 0.9962)^0 = 0.9886
so the required probability = 0.9886