Question

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.1 minutes and standard deviation 1.6 minutes. Suppose that a random sample of n=50 customers is observed. Find the probability that the average time waiting in line for these customers is

(a) Less than 10 minutes

(b) Between 5 and 10 minutes

(c) Less than 6 minutes

Round your answers to four decimal places (e.g. 0.9876).

Answer 1

Given

= 8.1 minutes

population standard deviation = 1.6 minutes

We have collected a sample of 50 customers

sample of 50 customers follows a distribution of N(8.1, 1.6/) = N(8.1, 0.226)

a) P(X<10 minutes)

Z = = = 8.407

P(X<10) = P(Z<8.407) = 1 .0000

b) Between 5 and 10 minutes

for X = 5, Z = -13.71

for X = 10, Z = 8.407

P(5<X<10) = P(-13.71<Z<8.407) = 1.0000

c) P(X<6)

for X = 6

Z = = -9.292

P(X<6) = P(Z<-9.292) = 0.0000