Question

The college cheerleader squad is seeking new members and requires applicants to meet a strict height requirement. The height of the college girls follows a normal distribution with mean of 5 feet and a standard deviation of 0.4 feet, i.e. N(5,0.4). Only girls whose height falls within the middle 20% of the distribution are eligible to apply. Doris is 4.9 feet tall and Susie is 5.1 feet tall. Can both of them apply? Explain your answer.

Answer 1

To determine if Doris and Susie can apply to the college cheerleader squad, we must calculate their z-scores and see if these scores fall within the middle 20% of the z-distribution.

Step-by-step explanation:

The question pertains to the application of normal distribution and specifically concerns the eligibility of two individuals based on their heights and the selection criteria for a college cheerleader squad. Assuming the heights are distributed normally with a mean of 5 feet and a standard deviation of 0.4 feet, we need to determine which percentage of the distribution falls between the heights of 4.9 feet (Doris) and 5.1 feet (Susie). The middle 20% of the distribution would define the eligibility range. To answer the question, we would need to calculate the z-scores for each girl's height and determine if these z-scores fall within the middle 20% of the z-distribution. If they do, both Doris and Susie can apply. If not, neither or only one of them may be eligible, depending on where their z-scores fall relative to the cut-off points for the middle 20%.