Question

The time it takes workers to finish cleaning is normally distributed with a mean of 73.27 minutes and a standard deviation of 7.04 minutes. If 13 workers are randomly selected, what is the probability the average time it takes them to finish cleaning is more than 73 minutes?

Answer 1

Here in this scenario it is given that the time it takes workers to finish cleaning is normally distributed with a mean of 73.27 minutes and a standard deviation of 7.04 minutes.

Now If we 13 workers are randomly selected then the probability the average time it takes them to finish cleaning is more than 73 minutes is given below,

Here note that the X fallowing the normal distribution with mean mu and sigma then,

Sampling Distribution samples mean xbar follows the normal with mean mu and sigma /√n.

The probability is calculated using Standerd normal distribution sampling Distribution for sample mean is calculated as below,

P(Xbar > 73) =

The probability is calculated using Standerd normal z-table.

The probability that the average time of 13 selected it takes them to finish cleaning is more than 73 minutes is 0.555.

Thank you.