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Chapter 6: Q6 (page 240)

Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.


Less than 4.00 minutes

Short Answer

Expert verified

The probability for waiting time larger than 3.00 minutes is 0.4.

Step by step solution

01

Given information

The graph for a uniform distribution is given with an area enclosed equally to 1.

02

State the relationship between area and probability

When the area under the density curve is 1, it can be assured that there is a one-to-one relationship between area and probability.

The probability that the waiting time is less than 4.00 minutes would be the same as the area of the shaded region shown below.

03

Find the probability

The probability that the waiting time is lesser than 4.00 minutes is the area of a rectangle with length 0.2 and width is 4-0=4units.

Thus,

PX<4.00=Length×widthoftheshadedarea=0.2×4=0.8

Thus, the probability of selecting a passenger randomly when the waiting time is lesser than 4.00 minutes is 0.8.

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Most popular questions from this chapter

In Exercises 9–12, find the indicated IQ score and round to the nearest whole number. 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).

In Exercises 13–20, 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, theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Mean

St.Dev.

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Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

For males, find P90, which is the length separating the bottom 90% from the top 10%.

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.

Greater than -2.00.

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.

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

z0.10
See all solutions

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