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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

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.

Ted is not particularly creative. He uses the pickupline 鈥淚f I could rearrange the alphabet, I鈥檇 put U and I together.鈥漈he random variable xis the number of women Ted approachesbefore encountering one who reacts positively.

x

P(x)

1

0.001

2

0.009

3

0.030

4

0.060

In Exercises 15鈥�20, refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.

Using Probabilities for Significant Events

a. Find the probability of getting exactly 6 girls in 8 births.

b. Find the probability of getting 6 or more girls in 8 births.

c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)?

d. Is 6 a significantly high number of girls in 8 births? Why or why not?

Number of girls x

P(x)

0

0.004

1

0.031

2

0.109

3

0.219

4

0.273

5

0.219

6

0.109

7

0.031

8

0.004

Identifying Binomial Distributions. In Exercises 5鈥�12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

Credit Card Survey In an AARP Bulletin survey, 1019 different adults were randomly selected without replacement. Respondents were asked if they have one or more credit cards, and responses were recorded as 鈥測es鈥� and 鈥渘o.鈥�

In Exercises 9鈥�16, use the Poisson distribution to find the indicated probabilities.

Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of deaths per corps-year, find the probability that a randomly selected corps-year has the following numbers of deaths: (a) 0, (b) 1, (c) 2, (d) 3, (e) 4. The actual results consisted of these frequencies: 0 deaths (in 144 corps-years); 1 death (in 91 corps-years); 2 deaths (in 32 corps-years); 3 deaths (in 11 corps-years); 4 deaths (in 2 corps-years). Compare the actual results to those expected by using the Poisson probabilities. Does the Poisson distribution serve as a good tool for predicting the actual results?

In Exercises 15鈥�20, refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children.

Use the range rule of thumb to determine whether 1 girl in 8 births is a significantly low number of girls.

Number of girls x

P(x)

0

0.004

1

0.031

2

0.109

3

0.219

4

0.273

5

0.219

6

0.109

7

0.031

8

0.004
See all solutions

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