Statistics and Probability Answers

The service time of the first service of a BMW is found to be normally distributed with a mean of 70 minutes and a standard deviation of 9 minutes. 

(a) If a customer brings her BMW in for its first service, calculate the probability that the car will be ready within one hour. Draw sketch of graph to show the area.  ​   (6) 

(b) Calculate the probability that the job will take more than an hour and a half. Draw sketch of graph to show the area. ​​​​​​            (5) 

(c) What percentage of first services will be completed between 50 and 60 minutes? Draw sketch of graph to show the area. ​​​​​  ​    (6) 

(d) The BMW dealer has a policy to give its customers a 15% discount on the cost of the first service if the service is not completed within 80 minutes. From a sample of 80 customers who brought their BMWs in for the first service how many are likely to receive the 15% discount? Illustrate your answer by sketch. ​  ​​    (7) 

Suppose a sample of 20 students were given a diagnostic test before studying a particular module and then again after completing the module. We want to find out if, in general, the module leads to improvements in students’ test scores. Use 5% level of significance. (the output range should be at cell G4)

Before Module: 17,18,15,10,9,6,25,8,29,34,19,35,22,20,19,27,17,20,22,21

After Module: 25,29,30,20,10,6,29,20,35,33,28,39,28,19,27,27,19,29,34,38

A warehouse has only one loading dock manned by a three person crew. Trucks arrive at the loading dock at an average rate of 5 trucks per hour and the arrival rate is Poisson distributed. The loading of a truck takes 10 minutes on an average and can be assumed to be exponentially distributed. The operating cost of a truck is Rs.20 per hour and the members of the loading crew are paid Rs.8 each per hour. Would you like to advise the truck owner to add another crew of 3 persons?

Research says that adult humans should drink 2 liters of water every day. However, the standard deviation is estimated at 0.7 liters. An event manager arranged 110 liters of mineral water for a one-day conference to be attended by 50 people. a. Present the distribution of population and the sample on a graph. b. Calculate the sample mean and standard error of mean. c. Calculate the probability that the event manager has sufficient water during the conference day.

Research says that adult humans should drink 2 liters of water every day. However, the standard deviation is estimated at 0.7 liters. An event manager arranged 110 liters of mineral water for a one-day conference to be attended by 50 people. a. Present the distribution of population and the sample on a graph. b. Calculate the sample mean and standard error of mean. c. Calculate the probability that the event manager has sufficient water during the conference day.