Question 4 (10 marks) The height of women in their twenties isnormally distributed with a mean 163 cm and a standard deviation of5 cm. A simple random sample of the population of women was takenwith a sample size of 36.

a) Find the mean and standard deviation of the samplingdistribution of sample mean height.

b) Find the approximate range of the sampling distribution.

c) Find the interquartile range of the samplingdistribution.

d) Find the probability that the sample mean height is between170cm and 174cm.