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Chapter 6: Q3 (page 240)
Standard Normal Distribution Identify the two requirements necessary for a normal distribution to be a standard normal distribution
The standard normal distribution has a mean of 0 and a standard deviation of 1.
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Standard normal distribution, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.
Greater than -3.75
Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers
to four decimal places.
Between -2.55 and -2.00.
Births: Sampling Distribution of Sample Proportion When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg (where b = boy and g = girl). Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?
In Exercises 11–14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in Coca-Cola Zero, Diet Pepsi, Dr Pepper, and Mellow Yello Zero.
Assume that random samples of size n = 2 are selected with replacement.
Sampling Distribution of the Range Repeat Exercise 11 using ranges instead of means.
Curving Test Scores A professor gives a test and the scores are normally distributed with a mean of 60 and a standard deviation of 12. She plans to curve the scores.
a. If she curves by adding 15 to each grade, what is the new mean and standard deviation?
b. Is it fair to curve by adding 15 to each grade? Why or why not?
c. If the grades are curved so that grades of B are given to scores above the bottom 70% and below the top 10%, find the numerical limits for a grade of B.
d. Which method of curving the grades is fairer: adding 15 to each original score or using a scheme like the one given in part (c)? Explain.
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