AP Stat Unit 1 Progress Check: MCQ Part B

The distribution of the amount of a customer's purchase at a convenience store is approximately normal, with mean $15.50 and standard deviation $1.72. Which of the following is closest to the proportion of customer purchase amounts between $14.00 and $16.00 ?

0.42

In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution?

1.5°F

The following table shows the number of miles a hiker walked on a trail each day for 6 days. What was the mean number of miles the hiker walked for the 6 days?

6.5

The following table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown. Which of the following statements is supported by the table and boxplot?

At least 75% of the people who attended the lecture were age 53 years or younger.

The distribution of the number of transactions performed at a bank each day is approximately normal with mean 478 transactions and standard deviation 64 transactions. Which of the following is closest to the proportion of daily transactions greater than 350 ?

0.977

To gather data for a statistics project, a student asked 10 friends how many hours of sleep they got on the previous night. The data are shown in the following list. What is the interquartile range (IQR) of the number of hours of sleep shown in the list?

3 hours

The following boxplot summarizes the heights of a group of people who participate in a weekend biking club. Which of the following statements is supported by the boxplot?

Approximately 50% of the people have a height between 62 inches and 70 inches.

A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the following is the best description of Gordo's and Flaco's weights?

Gordo's weight is classified as unhealthy but Flaco's weight is not.

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported? I. The median is not likely to change. II. The range is not likely to change. III. The mean is likely to increase.

I and III only

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim?

No, there is only one outlier at 58 minutes.

The following table shows summary statistics, in thousands, for the number of electrical workers and the number of concrete workers in the construction industry each month for the past 5 years. Based on the 1.5×IQR rule for outliers, which of the following statements is a correct comparison of the two distributions?

The concrete distribution has at least one lower outlier, and the electrical distribution has no lower outliers.

Which of the following can be reasonably modeled by a normal distribution?

The heights of tomato plants that were all planted on the same day

A sociologist studying marriage customs collected data on the length of time, in months, between the proposal and wedding. The following boxplot and table give the five-number summary for couples in which at least one person was getting married for the first time and for couples in which both people had been previously married. Based on the summary statistics, which of the following statements is supported by the boxplots and table?

The interquartile range of length of time for first-time couples is greater than that of previously married couples.

Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout the country. The following histograms summarize the relative frequency for each type of catfish. Based on the histograms, which of the following is the best comparison of the means and the ranges for the two distributions?

The mean and range of the fingerling catfish are both greater than those of the large catfish.

The following boxplot summarizes the earnings made on one day at 45 movie theaters. Which of the following best compares the median movie theater earnings with the mean movie theater earnings?

The median is less than the mean because the distribution is likely skewed to the right.

The following list shows the number of goals scored by a soccer team in each of 9 games. How does the median number of goals scored compare with the mean number of goals scored?

The median is less than the mean by 1.

A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold in a region. The following histogram summarizes the reporter's data. For a presentation on the data collected, the reporter used the median of the distribution to describe the typical purchase price. Which of the following might explain the use of median to describe the typical purchase price?

There is an outlier between $80,000 and $85,000. Medians are resistant to outliers, while means are not.

The distribution of the number of moths captured per night by a certain moth trap is approximately normal with mean 103. If 28 percent of the captures fall below 76 per night, which of the following equations can be used to find σ, the standard deviation of the distribution?

−0.58=76−103 ------- σ