BADM 216.D1 Spring 2016 Final Exam Part 21. Exponential DistributionSuppose the time it takes for a mechanic to change the engine-oil and run themaintenance check of a car is exponentially distributed with a mean of 20 minutes.Please answer the following questions.(a) What is the probability that it will take a mechanic less than 10 minutes to finish thework?(b) What is the probability that it will take a mechanic between 5 and 25 minutes to finishthe work?[Hint: Please see Chap006 â Slides 45-50 for Exponential probability distribution.Please also see page 285-287 in the textbook.]2. Sampling DistributionA population has a mean of 200 and a standard deviation of 50. Suppose a sample ofsize 100 is selected and ̅ is used to estimate Âµ.a. What is the probability that the sample means will be within Â± 5 of the populationmean?b. What is the probability that the sample means will be within Â±10 of the populationmean?[Hint: Please see Chap007 â Slides 20 -35 for formula and example. Please also seepage 310-316 in the textbook.]3. Estimate IntervalThe makers of a soft drink want to identify the average age of its consumers. Asample of 55 consumers was taken. The average age in the sample was 21 years with asample standard deviation of 4 years(a) Construct a 95% confidence interval estimate for the mean of the consumersâage.(b) Suppose a sample of 71 was selected (with the same mean and the samplestandard deviation). Construct a 95% confidence interval for the mean of theconsumersâ age.[Hint: Please see Chap008 â Slides 24-29 for formula and example. Please also seepage 343-349 in the textbook.]4. Hypothesis TestingSome people who bought X-Game gaming systems complained about waiting toolong for delivery. The industry standard for such products is seven days. In a sampleof 20 units sold, the average time of delivery is 8.2 days. Assume the standarddeviation of the population of delivery time is 2.73 days. Please answer the followingquestions:(a) Develop appropriate null and alternative hypotheses such that rejection of H0 willsupport those customersâ argument.(b) Compute the test statistic.(c) Use either p-value or critical value approach to test the Hypothesis at 95%confidence level.[Hint: This is an One-tailed Hypothesis Testing. Please see Chap009 â Slides 17-30for detailed explanation. Please also see page 383-389 in the textbook.]5. Extra points.A sample of 81 account balances from a credit company showed an average dailybalance of $2,050. The standard deviation of the population is known to be $300.We are interested in determining if the mean of all account balances (i.e., populationmean) is significantly different from $2,000.Question: Using the p-value approach at 95% confidence, test the above hypotheses.Please type your answer and the steps of computation in a Word file. (Please DONOT just write the answer. Show the steps that you solve the problems. Partialcredit will be given based on your computation steps.) Please save the file asâBADM216 Final Part2_Your First Name_Your Last Name.docxâ and submitthrough Blackboard.Due Date: For graduating students, April 28th, 2016, Thursday, 11:00PM.Due Date: For Non-graduating students, May 5th, 2016, Thursday, 11:00PM.