Question

2. The amount of time that a drive-through bank teller spends on a customer is a random variable with a mean  minutes and a standard deviation  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

b) more than 3.5 minutes

Answer 1

Let X be the random variable which describes the amount of time that a drive-through bank teller spends on a customer, in minutes.

Given that

Mean = 3.2 minutes

S.D = 1.6 minutes

Now we have random sample of n = 64 , by central limit theorem the sampling distribution of mean will follow normal with mean = 3.2 and Standard error = 16 / sqrt(64) = 0.2

a) Probablity that mean time at teller window is at most 2.7 minutes =

= 0.0062 [standard normal table]

b) Probablity that mean time at teller window is more than 3.5 minutes

= 1 - 0.9332

=0.0668

please like)