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Chapter 5: Q3 (page 220)

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

Find the mean and standard deviation for the numbers of adults in groups of five who have credit cards.

Short Answer

Expert verified

The mean number of adults in groups of five who have credit cards is 3.7 adults.

The standard deviation for the number of adults in groups of five who have credit cards is1 adult.

Step by step solution

01

Given information

The number of randomly selected adults are n=5.

The probability of randomly selected adults that have a credit card is p=0.74.

02

Compute the mean

Let x represent the number of adults who have a credit card.

In the given scenario, the variable x will follow the binomial distribution.

The mean number of adults in groups of five who have credit cards is computed as,

μ=np=5×0.74=3.7

Therefore, the mean number of adults in groups of five who have credit cards is 3.7 adults.

03

Compute the standard deviation 

The standard deviation for the number of adults in groups of five who have credit cards is computed as,

σ=npq=5×0.74×0.26=0.9808≈1

Therefore, the standard deviation for the number of adults in group of five who have credit cards is 1 adult.

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Most popular questions from this chapter

In Exercises 6–10, 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.

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Does the table describe a probability distribution?

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2

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The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.

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b. Find the median.

c. Find the mode.

d. Find the range.

e. Find the standard deviation.

f. Find the variance.

g. Use the range rule of thumb to identify the values separating significant values from those that are not significant.

h. Based on the result from part (g), do any of the planets have a number of moons that is significantly low or significantly high? Why or why not?

i. What is the level of measurement of the data: nominal, ordinal, interval, or ratio?

j. Are the data discrete or continuous?

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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?
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