CH6-7 Review

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado?

• 6.75

• 7.82

• 10.33

• 11.97

• 61.17

A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W represent the total amount won, where W=X−15. What is the mean of W ?

• $10.50

• $4.50

• −$4.50

• −$6.50

• −$10.50

According to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. Let the random variableG represent the number of people selected to find one person who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?

• 0.47

• 0.69

• 1.55

• 2.00

• 2.13

Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait.

The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?

• A value randomly selected from the distribution of S is expected to be 4.66.

• In repeated sampling from the distribution of S, the average of the values will approach 4.66.

• For a sample of values randomly selected from the distribution of S, the average of the sample will be 4.66.

• The probability is 0.66 that a value randomly selected from the distribution of S will be close to the mean.

• For a sample of values randomly selected from the distribution of S, the average of the sample will vary from the population mean by no more than 4.66.

Let W represent the number of attempted experiments to get one experiment that is not successful.

The random variable W has a geometric distribution with mean 4 and standard deviation 3.5. Which of the following is the best interpretation of the standard deviation?

• A single value randomly selected from the distribution of W will vary from 4 by 3.5 attempted experiments.

• A single value randomly selected from the distribution of W will vary from 3.5 by 4 attempted experiments.

• Values of W typically vary from 4 by about 3.5 attempted experiments, on average.

• Values of W typically vary from 3.5 by about 4 attempted experiments, on average.

• The standard deviation of a random sample of values selected from the distribution of W will be 3.5 attempted experiments.

In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable C represent the number of households in the sample that had a computer. What are the mean and standard deviation of C?

• The mean is 85 households, and the standard deviation is 0.36 household.

• The mean is 144.5 households, and the standard deviation is 5.05 households.

• The mean is 144.5 households, and the standard deviation is 13.04 households.

• The mean is 170 households, and the standard deviation is 5.05 households.

• The mean is 170 households, and the standard deviation is 0.36 household.

A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?

• 0.023

• 0.046

• 0.159

• 0.317

• 0.977

A manufacturing company uses two different machines, A and B, each of which produces a certain item part. The number of defective parts produced by each machine is about 1 percent. Suppose two independent random samples, each of size 100, are selected, where one is a sample of parts produced by machine A and the other is a sample of parts produced by machine B. Which of the following is true about the sampling distribution of the difference in the sample proportions of defective parts?

• The mean is 0 and the distribution is approximately normal.

• The mean is 0 and the distribution will not be approximately normal.

• The mean is 0.01 and the distribution is approximately normal.

• The mean is 0.01 and the distribution will not be approximately normal.

• The mean is 1 and the distribution is approximately normal.

For which of the following is the shape of the sampling distribution of the sample mean approximately normal?

I. A random sample of size 5 from a population that is approximately normal

II. A random sample of size 10 from a population that is strongly skewed to the right

III. A random sample of size 60 from a population that is strongly skewed to the left

• I only

• III only

• I and II only

• I and III only

• I, II, and III

The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?

• 0.14

• 0.37

• 0.39

• 0.60

• 0.65