1. the Weights of the Eggs Produced by a Certain Breed of Hen Are Normally Distributed

CP Statistics Name: ______Mrs Wiltrout Date: ______Period: ______16.3 Practice 1. 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. a. What is the probability that one egg selected from a hen house will weigh more than 68 grams?

b. Consider a carton of 12 eggs to be a simple random sample (SRS) of hen's eggs. If you were to take a large number of samples of size n = 12, what would the mean and standard deviation be of these sample means?

c. What is the probability that the average weight of the 12 eggs in a carton selected at random will be more than 68 grams? Is this sample normally distributed—why?

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.

a. What is the probability that an individual selected will be less than 70 years old?

b. If a sample of 50 people from this region is selected, and the probability that the mean life expectancy will be less than 70 years.

c. In your own words, explain so that someone not in this class can understand why there is a difference between (a) and (b) & explain what you have to do differently CP Statistics Name: ______Mrs Wiltrout Date: ______Period: ______16.3 Practice 3. The average length of a hospital stay in the US is µ = 9 days with standard deviation of σ=3 days. Assume a simple random sample of 100 patients is obtained and the mean stay for 100 patients is obtained. What is the probability that the average length of stay for this group of patients will be less than 9.6 days? To answer this question, we usually think of the following steps:

a. What is the mean of the sampling distribution of for samples of size 100?

b. What is the standard deviation of the sampling distribution of ¯x for samples of size 100?

c. Is this sample normally distributed? Explain why or why not

d. What is the probability to obtain a sample mean less than 9.6 days?

4. A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a normal distribution with mean=303 ml and standard deviation s = 3 ml. a. What is the probability that a bottle contains less than 300 ml?

b. Now take a random sample of 10 bottles. What are the mean and standard deviation of the sample mean contents x-bar of these 10 bottles?

c. What is the probability that the sample mean contents of the 10 bottles is less than 300 ml? CP Statistics Name: ______Mrs Wiltrout Date: ______Period: ______16.3 Practice 5. Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) If any person is selected, find the probability of getting someone with an IQ of at least 133

b) What’s the sample mean ad standard deviation for a sample size of 200?

c) If 200 people are selected, find the probability that their mean IQ score is at least 133

6. Scores for males on the verbal portion of the SAT test are normally distributed with a mean of 509 and standard deviation of 112. Randomly selected males are given the Columbia Review Course before taking the SAT test. Assume that the course has no effect. a) How do you know the sample is normally distributed even though the sample size is less than 30?

b) If 16 males are randomly selected, find the probability that their mean score is at least 590?

7. A manufacturing process is designed to produce bolts with a 0.5 inch diameter. Once each day, a random sample of 36 bolts is selected and the diameters are recorded for quality control. If the resulting sample mean is less than 0.49 inches or greater than 0.51, the process is shut down for adjustment. The standard deviation for the diameter is 0.02 inches. a) What’s the mean and standard deviation for the sample?

b) Why is the sample normally distributed?

c) What’s the probability the manufacturing line will be shut down? CP Statistics Name: ______Mrs Wiltrout Date: ______Period: ______16.3 Practice

8. Suppose that the distribution for total amounts spent by students vacationing for spring break in Florida is normally distributed with a mean of $650 and a standard deviation of $120. a) What’s the probability any students selected spent more than 800?

b) What’s the probability a SRS of 10 students spent between $600 & $700.

9. Suppose the average credit card balance for young people is $650 with a standard deviation of $420. a) In a SRS of 100 couples, what is the probability that the mean outstanding credit card balance exceeds $700?

b) Why can we use a normal distribution for the sample?

10. The strength of paper coming from a manufacturing plant is known to be 25 pounds per square inch with a standard deviation of 2.3. In a SRS of 29 pieces of paper, what is the probability that the mean strength between 24.5 and 25.5 pounds per square inch?