Discuss the following:
Q1:The net sales and the number of employees for aluminum fabricators with similar characteristics are organized into frequency distributions. Both are normally distributed. For the net sales, the mean is $180 million and the standard deviation is $25 million. For the number of employees, the mean is 1,500 and the standard deviation is 120. Clarion Fabricators had sales of $170 million and 1,850 employees.
1. Convert Clarion's sales and number of employees to z values.
2. Locate the two z values.
3. Compare Clarion's sales and number of employees with those of the other fabricators
Q2: The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.
1. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
2. What percent of the garages take between 29 hours and 34 hours to erect?
3. What percent of the garages take 28.7 hours or less to erect?
4. Of the garages, 5 percent take how many hours or more to erect?
Q3: A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group, Inc., in Somers, New York, showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes.
1. What fraction of the calls last between 4.2 and 5 minutes?
2. What fraction of the calls last more than 5 minutes?
3. What fraction of the calls last between 5 and 6 minutes?
4. What fraction of the calls last between 4 and 6 minutues
5. As part of her report to the president, the Director of Communications would like to report the length of the longest (in duration) 4 percent of the calls. What is this time?
Q4: Shaver Manufacturing, Inc. offers dental insurance to its employees. A recent study by the Human Resource Director shows the annual cost per employee per year followed the normal distribution, with a mean of $1,280 and a standard deviation of $420 per year.
1. What fraction of the employees cost more than $1,500 per year for dental expenses?
2. What fraction of the employees cost between $1,500 and $2,000 per year?
3. Estimate the percent that did not have any dental expense.
4. What was the cost for the 10 percent of employees who incurred the highest dental expense?
Q5: Best Electronics, Inc. offers a "no hassle" returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.
1. In what percent of the days are there 8 or fewer customers returning items?
2. In what percent of the days are between 12 and 14 customers returning items?
3. Is there any chance of a day with no returns?
Q6: Most four-year automobile leases allow up to 60,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follows the normal distribution. The mean is 52,000 miles and the standard deviation is 5,000 miles.
1. What percent of the leases will yield a penalty because of excess mileage?
2. If the automobile company wanted to change the terms of the lease so that 25 percent of the leases went over the limit, where should the new upper limit be set?
3. One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?