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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

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?

Good Sample? A geneticist is investigating the proportion of boys born in the world population. Because she is based in China, she obtains sample data from that country. Is the resulting sample proportion a good estimator of the population proportion of boys born worldwide? Why or why not?

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.

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 1.50 and 2.50.

Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are

a. significantly high (or at least 2 standard deviations above the mean).

b. significantly low (or at least 2 standard deviations below the mean).

c. not significant (or less than 2 standard deviations away from the mean).
See all solutions

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