Recall the key concept from section 6.4 about the Central Limit Theorem:

Given:

1. Population (with any distribution) has meanand standard deviation.

2. Simple random samples all of sizenare selected from the population.

Requirements: Population has a normal distributionorn> 30:

For the following questions, please verify the conditions to apply the Central Limit Theorem:

1) The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 264 days and standard deviation 16 days. Consider 15 pregnant women from a rural area. Assume they are equivalent to a random sample from all women.

2)In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years. Consider a sample of 50 people from this region.

3) The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.Consider a carton of 12 eggs to be a simple random sample (SRS) of hen's eggs.