A large school district in southern California asked all its

A large school district in southern California asked all its eighth-graders to measure the length of their right foot at the beginning of the school year, as part of a science project. The data show that foot length is approximately Normally distributed with mean of 23.4 cm and a standard deviation of 1.7 cm. Suppose that 25 eighth-graders from this population are randomly selected. The distribution of the mean foot length in samples of 25 students is approximately Normal, A. with mean and standard deviation unknown. B. with mean 23.4 cm and standard deviation 1.7 cm. C. with mean 23.4 cm and standard deviation 0.068 cm. D. with mean 23.4 cm and standard deviation 0.34 cm.

Solution

By central limit theorem, they will have the same mean, u(X) = 23.4 cm.

They will have a standard deviation given by

sigma(X) = sigma/sqrt(n) = 1.7/sqrt(25) = 0.34.

Hence, it is OPTION D: with mean 23.4 cm and standard deviation 0.34 cm. [ANSWER, D]