4. Population mean of the distribution of heights of elderly English women is 160 cm. with a standard deviation of 6 cm. Distribution of heights is normally distributed. We take simple random samples of 16 women from this population. a) Can we assume that distribution of sample means x is normal? Why/ why not? Explain b) If possible find the probability that in a random sample of 16 elderly English women, the mean height is leas than 156 cm. 5. Population mean height for 3-year-old boys is 38 inches and population standard deviation is 3 inches. Assume that heights are normally distributed in the population. a) Find probability that a randomly chosen 3-year old boy is shorter than 36 inches. b) Find probability that in a randomly chosen sample of 15 3-year old boys mean height is less than 36 inches. We want P(x < 36). 6. Women have head circumferences that are normally distributed with a mean of 22.65 in. and a standard deviation of 0.8 in. Desktop