91Ó°ÊÓ

Determine the value of \(z\) so that the area under the standard normal curve a. in the right tail is \(.0250\) b. in the left tail is \(.0500\) c. in the left tail is \(.0010\) d. in the right tail is \(.0100\)

Let \(x\) be a continuous random variable that follows a normal distribution with a mean of 550 and a standard deviation of 75 . a. Find the value of \(x\) so that the area under the normal curve to the left of \(x\) is \(.0250\). b. Find the value of \(x\) so that the area under the normal curve to the right of \(x\) is \(.9345\). c. Find the value of \(x\) so that the area under the normal curve to the right of \(x\) is approximately \(.0275 .\) d. Find the value of \(x\) so that the area under the normal curve to the left of \(x\) is approximately . 9600 . e. Find the value of \(x\) so that the area under the normal curve between \(\mu\) and \(x\) is approximately \(.4700\) and the value of \(x\) is less than \(\mu .\) f. Find the value of \(x\) so that the area under the normal curve between \(\mu\) and \(x\) is approximately \(.4100\) and the value of \(x\) is greater than \(\mu\).

Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is \(2.4\) minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a \(50 \%\) discount on the charges. The company wants to limit this discount to at most \(5 \%\) of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

A study has shown that \(20 \%\) of all college textbooks have a price of \(\$ 184.52\) or higher. It is known that the standard deviation of the prices of all college textbooks is \(\$ 36.35 .\) Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Under what conditions is the normal distribution usually used as an approximation to the binomial distribution?

For a binomial probability distribution, \(n=25\) and \(p=.40\). a. Find the probability \(P(8 \leq x \leq 13)\) by using the table of binomial probabilities (Table I of Appendix C). b. Find the probability \(P(8 \leq x \leq 13)\) by using the normal distribution as an approximation to the binomial distribution. What is the difference between this approximation and the exact probability calculated in part a?

According to a Gallup poll, \(92 \%\) of Americans believe in God (Time, June 20,2011 ). Suppose that this result is true for the current population of adult Americans. What is the probability that the number of adult Americans in a sample of 500 who believe in God is a. exactly 445 b. at least 450 c. 440 to 470

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.

A machine at Kasem Steel Corporation makes iron rods that are supposed to be 50 inches long. However, the machine does not make all rods of exactly the same length. It is known that the probability distribution of the lengths of rods made on this machine is normal with a mean of 50 inches and a standard deviation of \(.06\) inch. The rods that are either shorter than \(49.85\) inches or longer than \(50.15\) inches are discarded. What percentage of the rods made on this machine are discarded?

Major League Baseball rules require that the balls used in baseball games must have circumferences between 9 and \(9.25\) inches. Suppose the balls produced by the factory that supplies balls to Major League Baseball have circumferences normally distributed with a mean of \(9.125\) inches and a standard deviation of \(.06\) inch. What percentage of these baseballs fail to meet the circumference requirement?