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Chapter 6: Q7 (page 226)

Using Normal Approximation. In Exercises 5鈥�8, do the following: If the requirements of np猢�5 andnq猢�5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np<5or nq<5, then state that the normal approximation should not be used.

Guessing on Standard TestsWith guesses and for a correct answer, findP(at least 6 correct answers).

Short Answer

Expert verified

The method of normal approximation should not be used.

Step by step solution

01

 Step 1: Given information

A sample of 20 guesses of answers on a test is considered. The probability of a correct answer is equal to 0.2.

02

Check the requirement necessary for normal approximation

It is required thatnp猢�5 and nq猢�5.

The values are computed below:

np=200.2=4<5

nq=201-0.2=16<5

As one of the requirements is not fulfilled, the normal approximation cannot be applied to compute the probability value.

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Most popular questions from this chapter

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 Sample Mean

a. After identifying the 16 different possible samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same. (Hint: See Table 6-3 in Example 2 on page 258.)

b. Compare the mean of the population {34, 36, 41, 51} to the mean of the sampling distribution of the sample mean.

c. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not?

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?

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

z0.02

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.

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 2.00.
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