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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

Using the Central Limit Theorem. In Exercises 5鈥�8, assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).

a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

In Exercises 11鈥�14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in鈥侰oca-Cola鈥俍ero,鈥侱iet鈥侾epsi,鈥侱r鈥侾epper,鈥俛nd鈥侻ellow鈥俌ello鈥俍ero.

Assume鈥倀hat鈥� random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.

In Exercises 13鈥�20, use the data in the table below for sitting adult malesand females (based on anthropometric survey data from Gordon, Churchill, et al.). Thesedata are used often in the design of different seats, including aircraft seats, train seats,theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Sitting Back-to-Knee Length (Inches)

Mean

St. Dev

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

Significance Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) 0.025 and a value is significantly low if P(x or less) 0.025. Find the female back-to-knee length, separating significant values from those that are not significant. Using these criteria, is a female back-to-knee length of 20 in. significantly low?

assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors (based on PPG Industries).Red Cars: Find the probability of exactly 14 red cars. Why can鈥檛 the result be used to determine whether 14 is a significantly high number of red cars?

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
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