Answer :
Final answer:
The percentage of female college cross-country runners who weigh between 114 and 138 pounds, given a mean of 122 pounds and a standard deviation of 8 pounds, is approximately 81.85%.
Explanation:
To answer the question: 'What percent of the runners who weigh between 114 pounds and 138 pounds?', we first have to find the z-scores of those weights. The z-score is a measure of how many standard deviations an element is from the mean. It can be calculated using the formula: z = (X - μ) / σ where X is the value, μ is the mean and σ is the standard deviation.
So, for 114 pounds, z = (114 - 122) / 8 = -1 and for 138 pounds, z = (138 - 122) / 8 = 2. Now we use these z-scores to find the corresponding percentile in a z-table, which gives us the probabilities of 0.1587 for -1 and 0.9772 for 2. The percent of runners who weigh between 114 pounds and 138 pounds is thus approximately the probability of 2 minus the probability of -1, i.e. 0.9772 - 0.1587 = 0.8185 or 81.85%.
Learn more about Normal Distribution here:
https://brainly.com/question/30390016
#SPJ11
