4. the following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models…

4. the following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. based on the boxplot, the top 25% 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\ntypical gas mileage (miles per gallon)\n5. an amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. the following boxplot shows the heights of a sample of people who entered the amusement park on one day. based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction? (a) 25% (b) 48% (c) 50% (d) 75% (e) 100%\n6. an airline recorded the number of on - time arrivals for a sample of 100 flights each day. the boxplot below summarizes the recorded data for one year. based on the boxplot, which of the following statements must be true?\nnumber of on - time arrivals\n(a) the range of the number of on - time arrivals is greater than 90.\n(b) the interquartile range of the number of on - time arrivals is 22.\n(c) the percent of days that had at least 80 on - time arrivals is greater than the percent of days that had at most 76 on - time arrivals.\n(d) the percent of days that had from 76 to 80 on - time arrivals is equal to the percent of days that had at most 76 on - time arrivals.\n(e) the difference between the median and the lower quartile for the number of on - time arrivals is less than 2.

4. the following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. based on the boxplot, the top 25% 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\ntypical gas mileage (miles per gallon)\n5. an amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. the following boxplot shows the heights of a sample of people who entered the amusement park on one day. based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction? (a) 25% (b) 48% (c) 50% (d) 75% (e) 100%\n6. an airline recorded the number of on - time arrivals for a sample of 100 flights each day. the boxplot below summarizes the recorded data for one year. based on the boxplot, which of the following statements must be true?\nnumber of on - time arrivals\n(a) the range of the number of on - time arrivals is greater than 90.\n(b) the interquartile range of the number of on - time arrivals is 22.\n(c) the percent of days that had at least 80 on - time arrivals is greater than the percent of days that had at most 76 on - time arrivals.\n(d) the percent of days that had from 76 to 80 on - time arrivals is equal to the percent of days that had at most 76 on - time arrivals.\n(e) the difference between the median and the lower quartile for the number of on - time arrivals is less than 2.

Answer

4.

Explanation:

Step1: Recall box - plot properties

In a box - plot, the right - hand side of the box represents the third quartile ($Q_3$), which means 75% of the data is below it and 25% of the data is above it.

Step2: Identify $Q_3$ value

From the gas - mileage box - plot, the value corresponding to the right - hand side of the box (third quartile) is 35. So the top 25% of the cars have a typical gas mileage of at least 35 miles per gallon.

Answer:

(d) 35

5.

Explanation:

Step1: Analyze the box - plot for height data

The minimum value of the height box - plot is around 46 inches, the first quartile ($Q_1$) is around 50 inches, the median is around 58 inches, the third quartile ($Q_3$) is around 62 inches, and the maximum is around 66 inches. The requirement is 48 inches.

Step2: Estimate the percentage

Since the minimum value is 46 inches and the first quartile is 50 inches, and the data is assumed to be relatively evenly distributed in the lower part of the data set, we can estimate that about 75% of the people meet the 48 - inch height requirement.

Answer:

(d) 75%

6.

Explanation:

Step1: Recall box - plot statistics

The minimum value of the on - time arrivals box - plot is around 70, the first quartile ($Q_1$) is around 76, the median is around 80, and the maximum is around 100.

Step2: Analyze each option

  • Option (a): The range is $100 - 70=30$, not greater than 90.
  • Option (b): The inter - quartile range (IQR) is $Q_3 - Q_1$. Since $Q_3$ is around 80 and $Q_1$ is around 76, $IQR = 80 - 76 = 4$, not 22.
  • Option (c): The percentage of days with at least 80 on - time arrivals is 50% (from the median), and the percentage of days with at most 76 on - time arrivals is 25% (from $Q_1$). The percentage of days with 76 - 80 on - time arrivals is $50%-25% = 25%$. So the percentage of days with at least 80 on - time arrivals is not equal to the percentage of days with at most 76 on - time arrivals.
  • Option (d): The percentage of days with 76 - 80 on - time arrivals is 25% (from the difference between the median and $Q_1$), and the percentage of days with at most 76 on - time arrivals is 25% (from $Q_1$). So the percentage of days with 76 - 80 on - time arrivals is equal to the percentage of days with at most 76 on - time arrivals.
  • Option (e): The median is around 80 and the lower quartile ($Q_1$) is around 76. The difference is $80 - 76=4$, not less than 2.

Answer:

(d)