Hi guys, need help with part (d).
"7.69 Brain Weights. 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.
Ans: Sample means follows a normal distribution with mean 1.40 and standard deviation 0.064.
b. Repeat part (a) for samples of size 12.
Ans: Sample mean follows a normal distribution with mean 1.40 and standard deviation 0.032.
c. Construct graphs similar to those shown in Fig. 7.4 on
page 311.
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.
Solution: "88.12%. Chances are 88.12% that the sampling error made in estimating the mean brain weight of all Swedish men by that of a sample of three Swedish men will be at most 0.1 kg."