4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of ...

12. A researcher is interested in studying people’s mean age in a certain region. If the population standard deviation is known to be 9 years and 2 year of error margin is allowed, find the minimum simple size the researcher needs to use, knowing that he is going to conduct his study using 90% confidence level. (Points : 6) Sample Size = 55 Sample Size = 102 Sample Size = 52 Sample Size = 144 

13. (TCO 6) Horse race time is found to be normally distributed with a mean value of 18 minutes and a standard deviation of 4 minutes. Horses whose race time is in the top 6% will not be eligible to participate in a second round. What is the lowers race time that makes a horse losses his eligibility to participate in a second round? (Points : 6) 26.6 11.8 24.2 20.3 

14. (TCO 5) A class containing 25 students 12 of them are females. In how many ways can we select a group of 6 male students? (Points : 6) 1716 665280 1235520 924 

15. (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 70,000 miles and a standard deviation of 7,000 miles. What is the probability of having a tire that lasts more than 80,000 miles? (Points : 6) 0.9236 0.0778 0.0764 1.43 

16. (TCO 10) A research shows that employee salaries at company XYX, in thousands of dollars, are given by the equation y-hat= 48.5 + 2.2 a + 1.5 b where ‘a’ is the years of experience, and ‘b’ is the education level in years. In thousands of dollars, predict the salary for an employee with 5 years experience and 16 years education level. (Points : 6) 52.5 59.5 83.5 69.5 

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. 

3. A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions correctly. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions. Show your calculations or explain how you found the probability. 

4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of $25. (a) Find the probability of having a utility bill between 120 and 180. (b) Find the probability of having a utility bill less than $120. (c) Find the probability of having a utility bill more than $210. 

5. (TCO 8) A Mall manager claims that in average every customer spends $52 per a single visit to the mall. To test this claim, you took a sample of 36 customers and found the sample mean to be $55 and the sample standard deviation to be $12. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. 

6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions. (a) Find a 95% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it. 

7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products. (a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval. (b) Interpret this confidence interval and write a sentence that explains it.