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Stat400Lec15(Ch5.6)_ans - STAT 400(Chapter 5.6 Spring 2012...

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STAT 400 (Chapter 5.6) Spring 2012 1. The true weight of “10 - pound” sacks of potatoes processed at a certain packaging house follows a normal distribution with mean of 10.1 pounds and standard deviation of 0.2 pounds. a) What is the probability that a sack weighs at least 10 pounds? P ( X 10 ) = 2 . 0 1 . 10 10 Z P = P ( Z 0.50 ) = 1 ( 0.50 ) = 1 0.3085 = 0.6915 . b) A random sample of 9 sacks is selected. What is the probability that the average weight of these 9 is at least 10 pounds? Case 2. Z X σ μ n . P ( X 10 ) = 9 2 . 0 1 . 10 10 Z P = P ( Z 1.50 ) = 1 ( 1.50 ) = 1 0.0668 = 0.9332 .
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2. A student commission wants to know the mean amount of money spent by college students for textbooks in one semester. Suppose the population mean is $450 and the population standard deviation is $40. A random sample of 625 students is taken. a) What is the probability that the sample mean will be less than $452?
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