Stats Unit 1 MC midterm exam

Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle? A. 16% on the small puzzle and 16% on the large puzzle B. 16% on the small puzzle and 84% on the large puzzle C. 32% on the small puzzle and 68% on the large puzzle D. 84% on the small puzzle and 84% on the large puzzle E. 84% on the small puzzle and 16% on the large puzzle

B. 16% on the small puzzle and 84% on the large puzzle

A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean? A. ∑(x−x¯)=(86−84)+(81−84)+(87−84)+(82−84) B. ∑|x−x¯|=|86−84|+|81−84|+|87−84|+|82−84| C. 2∑|x−x¯|=2[|86−84|+|81−84|+|87−84|+|82−84|] D. ∑(x−x¯)2=(86−84)2+(81−84)2+(87−84)2+(82−84)2 E. [∑|x−x¯|]2=[|86−84|+|81−84|+|87−84|+|82−84|]2

D. ∑(x−x¯)2=(86−84)2+(81−84)2+(87−84)2+(82−84)2

The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? A. 15 B. 20 C. 25 D. 35 E. 50

D. 35

The following table shows data for the 8 longest roller coasters in the world as of 2015. Which of the following variables is categorical A. Length B. Type C. Speed D. Height E. Drop

Type

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution? A. 26 inches B. 28 inches C. 30 inches D. 33 inches E. 34 inches

26

A researcher is studying a group of field mice. The distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of field mice with a weight greater than 33 grams? A. 0.023 B. 0.046 C. 0.954 D. : 0.977 E. 1.000

A. 0.023

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds? A. 0.17 B. 0.25 C. 0.36 D. 0.83 E. 0.95

A. 0.17

A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine? A. 19.3 millimeters B. 20.6 millimeters C. 22.1 millimeters D. 23.5 millimeters E. 24.9mm

B. 20.6 millimeters

One statistic calculated for pitchers in baseball is called the earned run average, or ERA. The following boxplots summarize the ERA for pitchers in two leagues, A and B. Based on the boxplots, which of the following statistics is the same for both leagues? A. The range B. The interquartile range C. : The median D. The minimum E. The maximum

B. The interquartile range

The following table shows summary statistics for the number of hours a group of students spent playing video games last Monday and last Saturday. Based on the summary statistics, which of the following gives the best comparison of the range and the interquartile range (IQR)(IQR) of the two days? A. The range and I Q R of hours played on Monday are both greater than the range and I Q R of hours played on Saturday. B. The range and I Q R of hours played on Monday are both less than the range and I Q R of hours played on Saturday. C. The range and I Q R of hours played on Monday are both equal to the range and I Q R of hours played on Saturday. D. The range of hours played on Monday is greater than the range of hours played on Saturday, and the I Q R of hours played on Monday is less than the I Q R of hours played on Saturday. E. The range of hours played on Monday is less than the range of hours played on Saturday, and the IQR of hours played on Monday is greater than the IQR of hours played on Saturday.

B. The range and IQRIQR of hours played on Monday are both less than the range and IQRIQR of hours played on Saturday.

One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for two sources of disturbances. Based on the histograms, which of the following correctly compares the two distributions? A. The median of the earthquake disturbances is equal to the median of the mining disturbances. B. he median of the earthquake disturbances is less than the median of the mining disturbances. C. The range of the earthquake disturbances is equal to the range of the mining disturbances. D. The range of the earthquake disturbances is less than the range of the mining disturbances. E. The mode of the earthquake disturbances is equal to the mode of the mining disturbances.

B. he median of the earthquake disturbances is less than the median of the mining disturbances.

For a certain online store, the distribution of number of purchases per hour is approximately normal with mean 1,200 purchases and standard deviation 200 purchases. For what proportion of hours will the number of purchases at the online store exceed 1,400 ? A. 68% B. 32% C. 16% D. 5% E. 2.5%

C. 16%

Which of the following describes a continuous variable? A. The number of items sold at a craft booth for one day B. The number of apps downloaded from a website one day C. The diameters of the tree trunks at an evergreen farm D. The number of baskets made by a basketball player E. The shoe sizes of all shoes on sale at a department store

C. The diameters of the tree trunks at an evergreen farm

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequency of students from each grade who participate in the community service activity. Which of the following is supported by the bar chart? A. The greatest number of participating students was in grade 9. B. The number of participating students in grade 6 was equal to the number of participating students in grade 7. C. The relative frequency of all participating students in grades 6 and 7 combined was 0.60. D. Grade 12 had the least relative frequency of participating students. E. Grade 11 had the greatest relative frequency of participating students.

D. Grade 12 had the least relative frequency of participating students.

The following dotplot shows the scores of 25 people who played an online trivia game. Which of the following statements is the best description of the distribution of scores? A. The distribution is roughly symmetric. B. The distribution is roughly uniform. C. The distribution is skewed left. D. The distribution is skewed right. E. The distribution is bimodal.

D. The distribution is skewed right.

The distribution of the number of transactions per day at a certain automated teller machine (ATM) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution? A. x¯=80;s=10 B. x¯=80;s2=10 C. x¯=80;σ=10 D. μ=80;σ=10 E. μ=80;s=10

D. μ=80;σ=10

Data will be collected on the following variables. Which variable can be considered discrete? A. The height of a person B. The weight of a person C. : The length of a person's arm span D. The time it takes for a person to solve a puzzle E. The number of books a person finished reading last month

E. The number of books a person finished reading last month

The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm.Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR rule for outliers, is there evidence to support the claim? A.Yes, because open parenthesis, maximum minus Q 3, close parenthesis is greater than open parenthesis, Q 1 minus minimum, close parenthesis . B. Yes, because 43 is greater than open parenthesis, Q 3 plus I Q R, close parenthesis . C. Yes, because 43 is greater than open parenthesis, Q 1 minus 1.5 times I Q R, close parenthesis . D. No, because 43 is not greater than open parenthesis, Q 3 plus 1.5 times I Q R, close parenthesis . E. No, because 43 is greater than (Q1−1.5×IQR).

No, because 43 is not greater than (Q3+1.5*IQR)

The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. Which of the following statements is not supported by the table? A. The number of student responses is 300. B. One-third of the students chose vanilla. C. One-third of the students chose chocolate or strawberry. D. One-fourth of the students chose mint chip or coffee. E. One-half of the students chose vanilla or chocolate.

One-half of the students chose vanilla or chocolate.

Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram? A. The distribution must have an outlier. B. The distribution has a region between two data values where no data were observed. C. The distribution is approximately normal. D. The distribution cannot be symmetric. E. The distribution must be bimodal.

The distribution has a region between two data values where no data were observed.

The following histogram shows the ages, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages? A. The mean and the median are equal in value because the distribution is symmetric. B. The mean is most likely less than the median because the distribution is skewed to the right. C. The mean is most likely less than the median because the distribution is skewed to the left. D. The mean is most likely greater than the median because the distribution is skewed to the right. E. The mean is most likely greater than the median because the distribution is skewed to the left.

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

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution? There were 770 entries with a score less than or equal to 68. There were at least 230 entries with a score of 77. There were 23% of the entries with a score less than or equal to 68. There were 77% of the entries with a score equal to 68. There were at least 77% of the entries with a score greater than 68.

There were 770 entries with a score less than or equal to 68.