Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches. Compute the probability that a simple random sample...

Problem:

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n = 10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).

Gestation period

The length of human pregnancies is approximately normally distributed with mean µ = 266 days and standard deviation σ = 16 days.

1. What is the probability a randomly selected pregnancy lasts less than 260 days?


2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?


3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?


4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?