Probability using normal distribution.
1. General: presume that x has a distribution with µ = 72 and σ = 8.
(a) If random sample of size n = 16 are selected, can we say anything about the xbar distribution of sample means?
(b) If the original x distribution is normal, can we say anything about the xbar distribution of random samples of size 16? Find P (68 ≤ x ≤73).
2. Vital Statistics: Heights of men the heights of 18 year old men are approximately normally distributed, with mean 68 inches and standard deviation 3 inches.
(a) What is the likelihood that an 18 year old man selected at random is between 67 and 69 inches tall?
(b) If random sampling of nine 18 year old men is selected, what is the probability that the mean height xbar is between 67 and 69 inches?
(c) Evaluate your answers for parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?