Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. Which of the following is the best description of a histogram of the weights of all 2,000 athletes?
A. Skewed to the right (positively skewed).
B. Skewed to the left (negatively skewed).
C. Approximately uniform and centered at 250 pounds.
D. Approximately normal and centered at 250 pounds.
E. Bimodal.

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fichoh fichoh · Answer 1 · 2021-08-17T15:08:05+02:00

The best description of the histogram for the 2000 athletes will BE a BIMODAL distribution because two distinct peaks will be formed by the

The distribution has two obvious groups; The OFFENCE and DEFENSE each of which has a NORMAL distribution.

For a NORMAL distribution, we have a peak centered in between to tails.

• The left tail of the offense class is about 150

• Centre or peak at 200

• Right tail at about 250

The right tail of the offense class correlates to the left tail of the defense class which ranges from of 250 to 350 with it's centre at 300.

An histogram in the form of the picture attached below will be obtained.

Hence, there are two distinct peaks and the right tail of one distribution is synonymous with the left tail of the other.

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