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Chapter 6: Q6 (page 240)

Continuous Uniform Distribution. In Exercises 5鈥�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脳widthoftheshadedarea=0.2脳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

Standard normal distribution. In Exercise 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 score. If using technology instead of Table A-2, round answers to four decimal places.

Less than -1.96

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

z0.04

In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Median

a. Find the value of the population median.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-3. (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not?

College Presidents There are about 4200 college presidents in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 college presidents are randomly selected, and the mean annual income is computed for each sample. a. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)?

b. What value do the sample means target? That is, what is the mean of all such sample means?

Requirements A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution?
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