18. A population consists of N 55 numbers: 1, 3, 5, 6, and 7. It can be shown that the mean and standard deviation for this population are m 54.4 and s 52.15, respectively.

a. Construct a probability histogram for this population.

b. Use the random number table, Table 10 in Appendix I, to select a random sample of size n510 with replacement from the population. Calculate the sample mean, x . Repeat this procedure, calculating the sample mean x for your second sample.

(hint: Assign the random digits 0 and 1 to the measurement x51; assign digits 2 and 3 to the measurement x53, and so on.)

c. To simulate the sampling distribution of x , we have selected 50 more samples of size n510 with replacement, and have calculated the corresponding sample means. Construct a relative frequency histogram for these 50 values of x . What is the shape of this distribution?

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