1. Consider a normal population with µ = 24 and s = 7.0. (A) Calculate the stand
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Question
1. Consider a normal population with µ = 24 and s = 7.0.
(A) Calculate the standard score for a value x of 24.
(B) Calculate the standard score for a randomly selected sample of 45 with = 24.
(C) Explain why the standard scores of 24 are different between A and B above.
2. Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 95 and 105.
4. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.72 seconds.
Answer each of the following (show all work):
(A) How many measurements should be made in order to be 98% certain that the maximum error of estimation will not exceed 0.5 seconds?
(B) What sample size is required for a maximum error of 1.0 seconds?
Explanation / Answer
1. (A) z = (24-24)/7 = 0 (B) (24-24)/[7/sqrt(45)] = 0 (C) They're not different. 2. normalcdf(95,105,100,20/sqrt(150)) = 0.9978 3. (A) 0.5 = 2.33*3.72/sqrt(n) sqrt(n) = 2.33*3.72/0.5 = 17.335 n = 301 (B) sqrt(n) = 2.33*3.72/1.0 = 8.6676 n = 75
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