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Chapter 5: Q10 (page 195)

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are notsatisfied.

In a Microsoft Instant Messaging survey, respondents were asked to choose the most fun way to flirt, and the accompanying table is based on the results.

x

P(x)

E-mail

0.06

In person

0.55

Instant message

0.24

Text message

0.15

Short Answer

Expert verified

The requirement that x is a numerical random variable is not satisfied.

Step by step solution

01

Given information

The probability distribution for the most fun way to flirt is provided.

02

Identify the requirements for a probability distribution

Letthe variable x represent the type of messaging.

The requirements are as follows.

1)The variablex is a numerical random variable,which is not satisfied as the variable cannot be expressed in the number form.

2)The sum of the probabilities is computed as

鈭�Px=0.06+0.55+0.24+0.15=1

Therefore, the sum of the probabilities is 1.

3) Each value of P(x) is between 0 and 1.

Thus, the requirement that x is a numerical random variable is not satisfied.

Therefore, the mean and standard deviation cannot be computed.

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Most popular questions from this chapter

Ultimate Binomial Exercises! Exercises 37鈥�40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities.

Perception and Reality In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was 43%. Assume that 43% of voters actually did vote for the winning candidate, and assume that 611 voters are randomly selected.

a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the 308 voters who said that they voted for the winner significantly high?

b. Find the probability of exactly 308 voters who actually voted for the winner. c. Find the probability of 308 or more voters who actually voted for the winner. d. Which probability is relevant for determining whether the value of 308 voters is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 308 voters who said that they voted for the winner significantly high?

e. What is an important observation about the survey results?

In Exercises 15鈥�20, assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n = eight trials, each with probability of success (correct) given by p = 0.20. Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than 3.

In Exercises 1鈥�5, assume that 74% of randomly selected adults have a credit card (based on results from an AARP Bulletin survey). Assume that a group of five adults is randomly selected.

If the group of five adults includes exactly 1 with a credit card, is that value

of 1 significantly low?

In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

Does the table describe a probability distribution?

x

P(x)

0

0+

1

0.006

2

0.051

3

0.205

4

0.409

5

0.328

In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

Based on the table, the standard deviation is 0.9 flight. What is the variance? Include appropriate units.

x

P(x)

0

0+

1

0.006

2

0.051

3

0.205

4

0.409

5

0.328
See all solutions

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