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Section 9.3 – Sample Means If the sample size is larger enough, then 1) x The mean of a sampling distribution of means 2) x n The standard deviation of a sampling distribution of means If a sample is taken from a population that has a normal distribution, then the sampling distribution of the means will also be normally distributed. Central Limit Theorem The average age of all lawyers is 43.6 years with a standard deviation of 5.1 years. If a law firm employs 50 lawyers, find the probability that the average of the group is greater than 44.2 years. The average labor costs for car repairs for a large chain of car repair shops is $48.25. The standard deviation is $4.20. Assume the variable is normally distributed. a. If a store is selected at random, find the probability that the labor cost will range between $46. and $48. b. If 20 stores are selected at random, find the probability that the mean of the sample will be between $46. and $48.