Question

A Pizza delivery business in a large city has determined that the amount of time that a customer spends waiting for their delivery order is normally distributed with a mean of 26.5 minutes and a standard deviation of 3 minutes. What is the probability that for a randomly chosen customer the amount of time spent waiting for their delivery is less than 30 minutes. Use the calculator to determine the probability. Write the calculator function.

A Pizza delivery business in a large city has determined that the amount of time that a customer spends waiting for their delivery order is normally distributed with a mean of 26.5 minutes and a standard deviation of 3 minutes. What is the probability that for 100 randomly chosen customers the mean amount of time spent waiting for their delivery is greater than 27 minutes. Use the calculator to determine the probability. Write the calculator function

Answer 1

Here it is given that distribution is normal with mean=26.5 and sd=3

We need to find

As distribution is normal we can convert x to z

For sample size n=100>30, hence as per central limit theorem distribution of sample mean is also normal

Now we need to find

As sample mean is normally distributed we can convert sample mean to z