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Guidelines to problems chapter 7 (ST210) Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama Exercise 7.28 It is given that population distribution is left skewed, that is it has elongated tail on the left hand side. If we draw a sample of size n=400 from such a population and compute the sample mean x then what will be distribution of x ? Since the sample size is large, by application of Central Limit Theorem, distribution of x is approximately normal x ~ N ( , / 400) Exercise 7.32 X= amount of time taken to deliver the lunch order. X~N( 6.7, 2.1) That is on the average they take 6.7 x minutes to deliver the lunch order with a standard deviation of 2.1 minutes. If we draw the samples of size 16 and compute distribution of x ? then what will be the Though the sample is small ( n=16), since the parent distribution is normal the distribution of x will be normal x ~ N( 6.7, 2.1/√16) Exercise 7.36 Its given in problem that X= weight of a person in a small town Average weight of all the persons in the town is µ = 133 lb , with a standard deviation of 24lb Also given that population is right skewed. If we draw samples of size 45 from this population, what would be the distribution of the sample mean? Though parent population is skewed, since we are drawing large samples (n=45), by application of central limit theorem, the distribution of sample mean is normal x ~N( 133, 24/√45)