#1 Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean inches and standard deviation inches. Compute the probability that a simple random sample of size results in a sample mean greater than 40 inches.

#1 a. Gestation period The length of human pregnancies is approximately normally distributed with mean = 266 days and standard deviation = 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?

#2 Problem According to the U.S. Department of Agriculture, the mean calorie intake of males 20 to 39 years old , with standard deviation . Suppose a nutritionist analyzes a simple random sample of males between the ages of 20 and 39 years old and obtains a sample mean calorie intake of calories. What is the probability that a random sample of 35 males between the ages of 20 and 39 years old would result in a sample mean of 2750 calories or higher? Are the results of the survey unusual? Why?

#2a. Oil change The shape of the distribution of time required to get an oil change at a 10-minute oil change facility is unknown. However, records indicate that the mean time for an oil change is = 11.4 minutes and the standard deviation = 3.2 minutes.

1. To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
2. What is the probability that a random sample of oil changes results in a sample mean time less than 10 minutes?

Fishing: Billfish Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In World Record Game Fishes (published by the International Game Fish Association), it was stated that in the Cozumel region, about 44% of strikes (while trolling) result in a catch. Suppose that on a given day a fleet of fishing boats got a total of 24 strikes. What is the probability that the number of fish caught was:

1. 12 or fewer?
2. 5 or more?
3. between 5 and 12?

Grocery Stores: New Products The Denver Post stated that 80% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 66 new products, what is the probability that within 2 years:

1. 47 or more fail?
2. 58 or fewer fail?
3. 15 or more succeed?
4. fewer than 10 succeed?

Crime: Murder What are the chances that a person that is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About 64% of the people who are murdered actually knew the person who committed the murder. (Chances: Risk and Odds in Everyday Life by James Burke) Suppose that a detective file in New Orleans has 63 current unsolved murders. What is the probability that:

1. at least 35 of the victims knew their murderers?
2. at most 48 of the victims knew their murderers?

Basic Computation: distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

Can we approximate the distribution by a normal distribution? Why? What are the values of?:

Can we safely approximate the distribution by a normal distribution? Why or why not?

Can we approximate the distribution by a normal distribution? Why? What are the values of?

Basic Computation: distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

Can we approximate the distribution by a normal distribution? Why? What are the values of?

Can we safely approximate the distribution by a normal distribution? Why or why not?