Due to your successful advertising campaign you have been able to increase your pizza deliveries by 20% over the last three months. So you are now trying to decide if you want to continue advertising free pizza if the delivery is not made within 30 minutes or less. You decide to do a few more calculations on the amount of pizza deliveries being made each month. Your records still show that 97% of the deliveries are still being made in 30 minutes or less. Now you are going to do some calculations for the delivery times for each week using the mean delivery time which is 23 minutes and the standard deviation which was 20 minutes.
a) Describe the sampling distribution of, the sample mean delivery time for a random sample of 120 deliveries. Is the sampling distribution normally distributed? Explain.
b) Calculate and for the sampling distribution of the sample mean when the sample size is 120.
c) What is the probability that the mean delivery time for a random sample of 120 deliveries is less than 30 minutes? Round 4 decimals.
d) What is the probability that a random sample of 120 deliveries has a mean delivery time greater than 30 minutes? Round 4 decimals.
e) Based on the information given and the calculations you did in part 1 and part 2 should you continue advertising that deliveries not made in 30 minutes or less are free? Explain using complete sentences.