Unit 5 Progress Check: MCQ Part A

The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard deviation 4 inches. Which of the following represents the middle 80 percent of the heights?

• 50 inches to 73.37 inches

• 62 inches to 78 inches

• 64.87 inches to 75.13 inches

• 66 inches to 74 inches

• 66.63 inches to 90 inches

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The distribution of the amount of water used per wash cycle, in gallons, by a particular brand of dishwasher during a wash cycle is approximately normal with mean 4 gallons and standard deviation 0.2 gallon. Which of the following is closest to the probability that more than 3.75 gallons are used for any wash cycle?

• 0.11

• 0.21

• 0.34

• 0.79

• 0.89

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The life span of a battery is the amount of time the battery will last. The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour. Suppose one battery will be selected at random. Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?

• 0.055

• 0.110

• 0.445

• 0.890

• 0.945

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Data were collected on the following variables. Which variable is LEAST likely to be approximated with a normal model?

• The distribution of heights of tomato plants growing at an agricultural center, where most heights cluster around the center and there are some very short and very tall heights

• The distribution of times that a certain brand of house paint lasts on a house, where the distribution is symmetric and bell-shaped

• The distribution of lengths of the trout living in a certain stream, where the distribution is unimodal and clustered around the center, and the left half is a mirror image of the right half

• The distribution of weights of mold samples growing in a laboratory, where the distribution is symmetric, unimodal, and does not have any outliers

• The distribution of ages, in years, of all the residents of a town, where the right tail of the distribution is longer than the left

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Felip recorded 75 numerical observations on a certain variable and then calculated the mean x¯ and the standard deviation s for the observations. To help decide whether a normal model is appropriate, he created the following chart.

In Felip’s chart, the letters a,b,c,d,e represent the number of observations falling in each interval. Which of the following lists of counts for a,b,c,d,e, respectively, is the best indicator that the variable can be modeled with a normal approximation?

• 1, 31, 11, 31, 1

• 2, 10, 51, 10, 2

• 3, 6, 12, 24, 30

• 40, 20, 10, 4, 1

• 15, 15, 15, 15, 15

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The mean and standard deviation of the sample data collected on continuous variable Y are −0.5 and 0.5, respectively. The following table shows the relative frequencies of the data in the given intervals.

Based on the table, is it appropriate to use the normal model to approximate the population distribution?

Responses

• Yes, because the sum of the relative frequencies is 1.00.

• Yes, because the distribution of relative frequencies indicates a symmetric distribution.

• No, because the value of 0 is not in the center of the distribution.

• No, because the distribution of relative frequencies does not indicate a bell shape.

• No, because the sample size and the population parameters are not known.

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A recent study reported that 1.5 percent of flights are canceled by major air carriers. Consider a simulation with 50 trials designed to estimate the number of canceled flights from a random sample of size 100, where the probability of success, a canceled flight, is 0.015.

Of the following dotplots, which best represents the possible results from the simulation described?

Responses

• 
• 
• 
• 

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An advertisement firm reports that the proportion of consumers who respond favorably to a certain advertisement is 0.70. Three simulations, A, B, and C, were designed to create a sampling distribution of a sample proportion from a population with proportion 0.70. Each simulation consisted of 2,500 trials. For each trial of a simulation, a sample of size n was selected at random, and the sample proportion was recorded. The value of n varied among the simulations. The following histograms summarize the results of the simulations.

Which of the following lists the simulations in order from the least sample size n to the greatest sample size n ?

• Simulation A, simulation B, simulation C

• Simulation A, simulation C, simulation B

• Simulation B, simulation A, simulation C

• Simulation B, simulation C, simulation A

• Simulation C, simulation A, simulation B

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An online news source reports that the proportion of smartphone owners who use a certain operating system is 0.216. Two simulations will be conducted to create a sampling distribution of the sample proportion from a population with proportion 0.216. Simulation A will consist of 1,000 trials with a sample size of 50. Simulation B will consist of 500 trials with a sample size of 100.

Which of the following describes the centers and variabilities that should be apparent in the distributions generated by simulation A and simulation B?

Responses

• The centers will be approximately equal, and the variabilities will roughly be equal.

• The centers will be approximately equal, and the variability of simulation A will be greater than the variability of simulation B.

• The centers will be approximately equal, and the variability of simulation A will be less than the variability of simulation B.

• The center of simulation A will be greater than the center of simulation B, and the variabilities will be approximately equal.

• The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be less than the variability of simulation B.

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Samples A and B were selected from the same population. The mean of sample A is equal to the mean of the population.

Which of the following statements must be true?

1. I. The mean of sample A is a point estimator for the mean of the population.

2. II. The mean of sample B is a point estimator for the mean of the population.

3. III. The mean of sample A is equal to the mean of sample B.

• I only

• II only

• III only

• I and II

• II and III

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