(a) What is the probability that a fisherman catches a spotted sea trout within

Question

(a) What is the probability that a fisherman catches a spotted sea trout within the legal limits? (b) Given that the length of a trout exceeds 17 inches, what is a conditional probability that it is within legal limits? (c) The fisherman caught a large spotted sea trout. He wants to know whether the length is in the top 5% of the lengths of spotted sea trout in that region. Find the length x for which only 5% of the spotted trout in this region will be larger than x. Answers: (a) 0.4772, (b) 0.441, (c) 28.58 inches. As reported in Runner's World magazine, the times of the finishers in the New Your City 10-km run are normally distributed with mean 61 minutes and standard deviation 9 minutes. (a) Determine the percentage of finishers with times between 50 and 70 minutes. (b) Determine the percentage of finishers with times greater than 75 minutes. (c) Given that a runner's finishing time is below 70 minutes, what is a conditional probability that his finishing time exceeds 55 minutes. (d) Given that a runner's finishing time exceeds 60 minutes, what is a conditional probability that his finishing time is below 75 minutes. (e) Determine and interpret the quartiles for the finishing times. Answers: (a) 0.7301, (b) 0.0594, (c) 0.7012, (d) .8908, (e) 54.97, 61, and 67.03 minutes. Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. (a) If a school only admits students who score over 680, what proportion of student pool would be eligible for admission? (b) What should be the limit if only the top 15% are to be eligible? Answers: (a) 0.0359, (b) 604 Suppose that the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation of 0.4 ounce. (a) If every can is labeled 32 ounces, what proportion of the cans have contents that weigh less than the labeled amount? (b) If two cans are randomly selected, what is the probability that the average weight is less than 32 ounces? Answers: (a) 15.87%, (b) 0.0793 The lengths of the trout fry in a pond fish hatchery are approximately normally distributed with the mean 3.4 inches and standard deviation of 0.8 inches. Three dozen fry will be netted and their lengths measured. What is the probability that the sample mean length of 36 trout fry will be less than 3.2 inches? Answer: 0.0668.

Explanation / Answer

11) Mean,µ = 32.4 ounces Standard Deviation, = 0.4 ounces a) P(X

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