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Chapter 6: Q2 (page 240)

Normal Distribution A normal distribution is informally described as a probability distribution that is 鈥渂ell-shaped鈥� when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.

Short Answer

Expert verified

The rough sketch of the normal curve is shown below.

Step by step solution

01

Given information

A normal distribution is bell-shaped.

02

Define a normal distribution

A normal distribution shows a bell shape where the curve rises from left to right, reaching the height at the mean value and then decreasing symmetrically.

03

Step 3:Sketch the normal curve

The sketch of a normal curve is shown below.

The graph is sketched on two axes; the values of a random variable and the corresponding values of the random variables of normal distribution and the probabilities.

The graph is sketched below.

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Most popular questions from this chapter

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

Mean

St.Dev.

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

For females, find the first quartile Q1, which is the length separating the bottom 25% from the top 75%.

Standard Normal DistributionIn Exercises 17鈥�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 2.00 and 3.00.

Standard Normal Distribution. Find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

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 = -1 and z = 1 (or within 1 standard deviation of the mean).

Water Taxi SafetyWhen a water taxi sank in Baltimore鈥檚 Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a 鈥渨orst-case鈥� scenario in which all of

the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).

a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board).

b. With a load limit of 3500 lb, how many male passengers are allowed if we assume a mean weight of 140 lb?

c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb?

d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?
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