1-A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is4inches. A random sample of58fish is taken from the tank. Letxbe the mean sample length of these fish. What is the probability thatxis within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

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The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of8.5minutes and a standard deviation of2.9minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes (b) longer than 5 minutes (c) between 8 and 15 minutes

3-Findzsuch that57%of the standard normal curve lies betweenzandz. (Round your answer to two decimal places.)

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In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you take the free samples offered in supermarkets? About62%of all customers will take free samples. Furthermore, of those who take the free samples, about39%will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples,313customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample? (b) What is the probability that fewer than 200 will take your free sample? (c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule fordependentevents. Notice that we are given the conditional probabilityP(buy|sample) =0.39,whileP(sample) =0.62. (d) What is the probability that between 60 and 80 customers will take the free sampleandbuy the product?Hint:Use the probability of success calculated in part (c).

A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean= 38minutes and standard deviation= 5 minutes.

(a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (Round your answer to four decimal places.) (b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (Round your answer to four decimal places.) (c) Comment on the differences of the results in parts (a) and (b).The probability in part (b) is ---Select--- the same as larger than smaller than the probability in part (a) because the ---Select--- mean standard deviation is ---Select--- larger smaller for thexdistribution.

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According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation? % Within 2 standard deviations? % Within 3 standard deviations? %