Final answer:
To determine if Doris and Susie can apply to the cheerleader squad based on the height requirement, their heights would need to fall within the middle 20% of the normal distribution. This is determined by calculating the z-scores for their respective heights and seeing if these scores fall between the 40th and 60th percentiles.
Step-by-step explanation:
The question requires an understanding of the properties of normal distribution and how to determine which individuals fall within a certain percentile range. Given that the college girls' height follows a normal distribution with a mean of 5 feet and standard deviation of 0.4 feet, only those whose height falls within the middle 20% of this distribution can apply to the cheerleader squad.
To determine this, we would find the z-scores for Doris and Susie's heights, which are 4.9 feet and 5.1 feet, respectively. The z-score is a measure of how many standard deviations an element is from the mean. Because we are looking for the middle 20%, we are interested in the range of heights that fall between the 40th and 60th percentiles of the normal distribution.
If we calculate the z-scores for the heights of Doris and Susie and find that their heights are between the 40th and 60th percentiles, then they both can apply. However, if either of their heights falls outside this range, they would not meet the height requirement. Unfortunately, without further calculation using z-tables or a statistical software package, we cannot definitively say whether Doris and Susie can apply.