# ESTIMATE THE MEAN NUMBER OF TRANSACTIONS BUSINESSES

11. (TCO 3) The grades of 22 students are listed below. Use the stem & leaf to determine the shape of the distribution. Choose the best answer. 4 | 7 5 5 | 1 7 5 6 | 5 6 7 8 9 7 | 1 6 7 8 8 9 8 | 2 4 7 6 9 | 4 7 a. The data is symmetric b. The data is skewed to the right c. The data is skewed to the left d. The data is bimodal

12. A researcher is interested in studying people’s mean age in a certain region. If the population standard deviation is known to be 8 years and 1.5 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 95% confidence level. 110

13. Horse race time is found to be normally distributed with a mean value of 10 minutes and a standard deviation of 2 minutes. Horses whose race time is in the top 5% 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? 13.29 minutes

14. A class containing 15 students 5 of them are females. In how many ways can we select a group of 4 male students? 210 ways

15. 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? 0.0766

16. 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. 83.5

1. For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim. A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel.

2. A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the manager’s claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.

3. A researcher found that 85% of customers who make purchase at a department store are pleased with the store customer service. We asked 20 customers whether or not they are please with the store customer service. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability that, out of 20 customers, exactly 12 of them are pleased with the store customer service. Show your calculations or explain how you found the probability.

4. The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20. (a) Find the probability of having a utility bill between 135 and 170. (b) Find the probability of having a utility bill less than $135. (c) Find the probability of having a utility bill more than $180.

5. A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. 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. A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 55 businesses, he found that mean number of transaction per month to be 32 and the standard deviation to be 7.5 transactions. (a) Find a 90% 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. 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.

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