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Chapter 6: Q3 (page 250)

What is the difference between a standard normal distribution and a non-standard normal distribution?

Short Answer

Expert verified

The two parameters, the mean and the standard deviation of a standard normal distribution, are 0 and 1, respectively, while the parameters of non-standard normal distribution may have a different combination of values.

Step by step solution

01

Given information

The distributions provided are a standard normal distribution and a non-standard normal distribution.

02

Describe a normal distribution

A normal distribution refers to a probability distribution of a random variable, which is shaped like a bell such that it has the axis of symmetry aligned with the mean value. Depending on the change of the mean and standard deviation value, the shape varies for the family of curves.

03

State the difference

The standard normal distribution is a normal curve with the combination of the parameters:the mean as 0 and the standard deviation as 1.

The non-standard normal distribution is a distribution where the mean and standard deviation appear in some other combination.

Thus, the shape of the standard normal curve is considered ideal.

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Most popular questions from this chapter

Quarters After 1964, quarters were manufactured so that their weights have a mean of5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you canadjust the weights of quarters that are accepted. If many counterfeit coins are found, you cannarrow the range of acceptable weights with the effect that most counterfeit coins are rejectedalong with some legitimate quarters.

a. If you adjust your vending machines to accept weights between 5.60 g and 5.74 g, what percentage of legal quarters are rejected? Is that percentage too high?

b. If you adjust vending machines to accept all legal quarters except those with weights in the top 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted?

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?

Standard Normal Distribution Identify the two requirements necessary for a normal distribution to be a standard normal distribution

Sampling Distribution Data Set 4 鈥淏irths鈥� in Appendix B includes a sample of birth weights. If we explore this sample of 400 birth weights by constructing a histogram and finding the mean and standard deviation, do those results describe the sampling distribution of the mean? Why or why not?

Critical Values. In Exercises 41鈥�44, find the indicated critical value. Round results to two decimal places.

z0.04
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