5. A new community park is being built in a neighborhood. The park will be developed on an open rectangular plot of land that is 500 yards long and 250 yards wide. Three paths will be built in the park that all connect at the center of the park. The layout of the park and the paths are shown in the diagram below. The lengths of only two of the paths are given. Find the length of the third path.

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. complete parts (a) through (c) below. a. if 1 adult female is randomly selected, find the probability that her pulse rate is between 65 beats per minute and 79 beats per minute. the probability is? b. if 16 adult females are randomly selected, find the probability that they have pulse rates with a mean between 65 beats per minute and 79 beats per minute. the probability is? c. why can the normal distribution be used in part (b), even though the sample size does not exceed 30?