Answer :
To find the percent of female college cross-country runners who weigh between 114 pounds and 138 pounds, we calculate the z-scores for each weight and refer to the standard normal distribution table. The result is approximately 82% of the distribution. Therefore correct option is D
The question is asking what percent of female college cross-country runners weigh between 114 pounds and 138 pounds if the weights are normally distributed with a mean of 122 pounds and a standard deviation of 8 pounds.
To find the percentage, we will need to calculate the z-scores for both 114 pounds and 138 pounds and then refer to the standard normal distribution table.
To calculate the z-scores:
- For 114 pounds: z = (114 - 122) / 8 = -1
- For 138 pounds: z = (138 - 122) / 8 = 2
Looking at the standard normal distribution table, the area between z = -1 and z = 2 (which corresponds to the weights between 122-8=114 pounds and 122+16=138 pounds) captures about 81.85% of the distribution. This area is approximately equal to the sum of the areas from the left of z = 2 (which is roughly 97.72%) and the left of z = -1 (which is roughly 15.87%), then we subtract the latter from the former. However, the closest available answer choice is 82%, which is answer choice d.
