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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

Short Answer

Expert verified

The standard normal distribution has a mean of 0 and a standard deviation of 1.

Step by step solution

01

Given information

A standard normal distribution

02

Define a normal distribution

A normal distribution is a simple bell-shaped curve that attains maximum value and symmetry at a mean measure of the distribution.

It has two parameters: mean and standard deviation.The family of normal curves forms with varying means and standard deviation measures.

One of such is a standard normal curve with a mean of 0 and a standard deviation of 1.

Thus, a standard normal distribution must fulfill two requirements:

  • Mean 渭of 0
  • Standard deviation蟽 of 1

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Most popular questions from this chapter

Finding Bone Density Scores. In Exercises 37鈥�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 P10, the 10th percentile. This is the bone density score separating the bottom 10% from the top 90%.

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -2 and z = 2 (or within 2 standard deviation of the mean).

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

In Exercises 5鈥�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).
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