Question

The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.9 cm

a. Find the probability that an individual distance is greater than 217.50 cm.

b. Find the probability that the mean for 25 randomly selected distances is greater than 202.80 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Answer 1

(c) We can use the normal distribution in part (b), even if the sample size did not exceed 30, because the underlying distribution of X is normally distributed. Hence, the distribution of the sample mean is also normally distributed, whatever be the sample size.