Question

the final team showdown at a hotdog eating competition was between jerrys team and bens team. the distributions of the number of hotdogs eaten by members of each team in the showdown are shown in the box plots. members of jerrys team members of bens team 10 12 14 16 18 20 22 24 number of hotdogs eaten a most of the members of jerrys team ate lower hotdogs than most of the members of bens team. b at least one member of jerrys team ate more hotdogs than every member of bens team. c the range of the number of hotdogs eaten by members of jerrys team was greater than the range of the number of hotdogs eaten by members of bens team. d every member of jerrys team ate more hotdogs than at least half of the members of bens team.

Explanation:

Step1: Understand box - plot properties

A box - plot shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values.

Step2: Analyze Option A

For Jerry's team, the box and whiskers are mostly in the higher range compared to Ben's team. So, it is not true that most of Jerry's team ate fewer hot - dogs than most of Ben's team.

Step3: Analyze Option B

The maximum value of Jerry's team is greater than the maximum value of Ben's team. So, at least one member of Jerry's team ate more hot - dogs than every member of Ben's team.

Step4: Analyze Option C

The range is calculated as $Range = Maximum - Minimum$. For Jerry's team, the range is smaller than that of Ben's team.

Step5: Analyze Option D

The minimum value of Jerry's team is not greater than $Q_2$ of Ben's team. So, it is not true that every member of Jerry's team ate more hot - dogs than at least half of the members of Ben's team.

Answer:

B. At least one member of Jerry's Team ate more hotdogs than every member of Ben's Team.