The following assignment will allow you to master the material on Normal Distributions & Sampling Distributions.
1. It is very important to be able to find probabilities for a given z score. Using software or a Standard Normal Distribution table, determine the following probability for the area (15 points)
a. between z = -0.52 and z = 2.33
b. z > 1.65
c. z < 1.85
d. z < 0
e. between z = 0 and z = 1
2. Answer the following: (15 points)
a. If samples of a specific size are selected from a population and the means are computed, what is the distribution of the means called?
b. Why do most of the sample means differ somewhat from the population mean? What is this difference called?
c. What is the mean of the sample means?
d. What is the standard deviation of the sample means called? What is the formula for this standard deviation?
e. What does the central limit theorem say about the shape of the distribution of sample means?
3. A pediatrician obtains the heights of her 200 three-year-old female patients. The heights are normally distributed with a mean of 37.8 and a standard deviation of 3.14. What percent of the three-year-old females have a height less than 34 inches? (15 points)
4. The local news reported that 6% of U.S. drivers text on their cell phones while driving. If 300 drivers are selected at random, find the probability that exactly 25 say they text while driving. Be sure and use the continuity correction for the normal approximation to the binomial distribution. (15 points)
5. Suppose you are asked to toss a coin 16 times and calculate the proportion of the tosses that were heads. (10 points)
a. What shape would you expect this histogram to be and why?
b. Where you do expect the histogram to be centered?
c. How much variability would you expect among these proportions?
d. Explain why a Normal model should not be used here.
6. The average cholesterol content of a certain brand of eggs is 210 milligrams, and the standard deviation is 14 milligrams. Assume the variabe is normally distributed. If two eggs are selected, find the probability that the cholesterol content will be greater than 230 milligrams. (10 points)
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