The height of women in their twenties is normally distributed with a mean 163 cm and a standard deviation of 5 cm. A simple random sample of the population of women was taken with a sample size of

36.

1. Find the mean and standard deviation of the sampling distribution of sample mean height.
2. Find the approximate range of the sampling distribution.
3. Find the interquartile range of the sampling distribution.
4. Find the probability that the sample mean height is between 170cm and 174cm.