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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Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density 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 bone density test score corresponding to the given information. Round results to two decimal places.
Find the bone density scores that can be used as cutoff values separating the lowest 3% and highest 3%.
In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).
Birth Weights Based on Data Set 4 “Births” in Appendix B, birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g.
a. For the bell-shaped graph, what is the area under the curve?
b. What is the value of the median?
c. What is the value of the mode?
d. What is the value of the variance?
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?
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