BADM 216.D46 Fall 2016 1. Exponential Distribution Suppose the time it takes for a mechanic to change the engine-oil and run the maintenance 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 the work? (b What is the probability that it will take a mechanic between 5 and ) 25 minutes to finish the work? [Hint: Please see Chap006 - Slides 45-50 for Exponential probability distribution. Please also see page 285-287 in the textbook.] 2. Sampling Distribution A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimate . a. What is the probability that the sample means will be within 5 of the population mean? b. What is the probability that the sample means will be within 1 0 of the population mean? [Hint: Please see Chap007 - Slides 20 -35 for formula and example. Please also see page 310-316 in the textbook.] 3. Estimate Interval The makers of a soft drink want to identify the average age of its consumers. A sample of 55 consumers was taken. The average age in the sample was 21 years with a sample standard deviation of 4 years (a)Construct a 95% confidence interval estimate for the mean of the consumers' age. (b Suppose a sample of 71 was selected (with the same mean ) and the sample standard deviation). Construct a 95% confidence interval for the mean of the consumers' age. [Hint: Please see Chap008 - Slides 24-29 for formula and example. Please also see page 343-349 in the textbook.] 4. Hypothesis Testing Some people who bought X-Game gaming systems complained about waiting too long for delivery. The industry standard for such products is seven days. In a sample of 20 units sold, the average time of delivery is 8.2 days. Assume the standard deviation of the population of delivery time is 2.73 days. Please answer the following questions: (a Develop appropriate null and alternative hypotheses such that ) rejection of H0 will support those customers' 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 - Slides 17-30 for 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 daily balance 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., population mean) is significantly different from $2,000. Questi Using the p-value approach at 95% confidence, test the on: above hypotheses. Please type your answer and the steps of computation in a Word file. (Please DO NOT just write the answer. Show the steps that you solve the problems. Partial credit will be given based on your computation steps.) Please save the file as \"BADM216.D46 Final Part2_Your First Name_Your Last Name.docx\" and submit through Canvas