1. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces:
Exactly 5 will be defective?
5 or more will be defective?
2. Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that:
None of the antennas is defective.
Three or more of the antennas are defective.
3. 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.
a.Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
b.What percent of the garages take between 29 hours and 34 hours to erect?
c.What percent of the garages take 28.7 hours or less to erect?
d.Of the garages, 5 percent take how many hours or more to erect?
4. 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 probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.
a.What fraction of the employees cost more than $1,500 per year for dental expenses?
b.What fraction of the employees cost between $1,500 and $2,000 per year?
c.Estimate the percent that did not have any dental expense.
d.What was the cost for the 10 percent of employees who incurred the highest dental expense?
The solution is comprised of detailed step-by-step calculation and explanation of the various problems related to Probability. This solution provides students with a clear perspective of the underlying mathematical aspects.