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The management at Ohio National Bank does not want its customers to wait in line for service for too long. The manager of a branch of this bank estimated that the customers currently have to wait an average of 8 minutes for service. Assume that the waiting times for all customers at this branch have a normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes a. Find the probability that a randomly selected customer will have to wait for less than 3 minutes. b. What percentage of the customers have to wait for 10 to 13 minutes? c. What percentage of the customers have to wait for 6 to 12 minutes? d. Is it possible that a customer may have to wait longer than 16 minutes for service? Explain.

The print on the package of 100 -watt General Electric soft-white lightbulbs states that these bulbs have an average life of 750 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 750 hours and a standard deviation of 50 hours. a. Let \(x\) be the life of such a lightbulb. Find \(x\) so that only \(2.5 \%\) of such lightbulbs have lives longer than this value. b. Let \(x\) be the life of such a lightbulb. Find \(x\) so that about \(80 \%\) of such lightbulbs have lives shorter than this value.

Stress on the job is a major concern of a large number of people who go into managerial positions. It is estimated that \(80 \%\) of the managers of all companies suffer from job-related stress. a. What is the probability that in a sample of 200 managers of companies, exactly 150 suffer from job-related stress? b. Find the probability that in a sample of 200 managers of companies, at least 170 suffer from job-related stress. c. What is the probability that in a sample of 200 managers of companies, 165 or fewer suffer from job-related stress? d. Find the probability that in a sample of 200 managers of companies, 164 to 172 suffer from job-related stress.

Lori just bought a new set of four tires for her car. The life of each tire is nomally distributed with a mean of 45,000 miles and a standard deviation of 2000 miles. Find the probability that all four tires will last for at least 46,000 miles. Assume that the life of each of these tires is independent of the lives of other tires.

The amount of time taken by a bank teller to serve a randomly selected customer has a normal distribution with a mean of 2 minutes and a standard deviation of \(.5\) minute. a. What is the probability that both of two randomly selected customers will take less than I minute each to be served? b. What is the probability that at least one of four randomly selected customers will need more than \(2.25\) minutes to be served?