# Normal Distribution and Probability

1. Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with mean = 6 ounces and standard deviation= 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

a) The mean of the sampling distribution is 6 ounces.

b) The standard deviation of the sampling distribution is 2.5 ounces.

c) The shape of the sample distribution is approximately normal.

d) All of the above are correct.

please, explain.

2. 10. Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million.

please, explain.

thanks.

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#### Solution Preview

(1) A is true because the mean of the sampling distribution (of all samples) tends to the population mean as n increases.

B is not true. The standard deviation of the sample is not necessarily equal to the ...

#### Solution Summary

Both questions solved methodically.