Question: In 1905 R Pearl published the article Biometrical Studies on

In 1905, R. Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of Swedish men are normally distributed with a mean of 1.40 kg and a standard deviation of 0.11 kg.
a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three Swedish men.
b. Repeat part (a) for samples of size 12.
c. Construct graphs similar to those shown in Fig. 7.4 on page 293.
d. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.40 kg. Interpret your answer in terms of sampling error.
e. Repeat part (d) for samples of size 12.

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