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In 1905, R. Pearl published the article "Biometrical Studies on Man. 1. Variation and Correlation in...

In 1905, R. Pearl published the article "Biometrical Studies on Man. 1. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp13-104). According to the study, brain weights of Swedish men are normally distributed with a mean of 1.4 kg and a standard deviation of 0.11 kg.

A.) What is the probability a randomly selected swedish man will have a brain weighing more than 1.5 kg?

B.) Determine the sampling distribution of the sample mean brain weight for the samples of n = 3 Swedish men.

C.) What is the probability that the sample mean from such a sample will be larger than 1.5 kg?

D.) Repeat part b. For sample size n = 12.

E.) What is the probability that the sample mean from the sample of this size (n = 12) will be larger than 1.5 kg?

F.) Explain why the probabilities calculated in parts a., c., and e. become progressively smaller.

Math   Statistics-And-Probability   
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