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A survey found that women's heights are normally distributed with mean 62.8 in. and standard deviation 3.2 in. The survey also found that men's heights are normally distributed with mean 69.6 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in and a maximum of 63 in. Complete parts (a) and (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park? The percentage of men who meet the height requirement is %. (Round to two decimal places as needed.) Since most men the height requirement, it is likely that most of the characters are b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements? in. The new height requirements are a minimum of in and a maximum of| (Round to one decimal place as needed.)
Assume that females have pulse rates that are normally distributed with a mean of p = 72.0 beats per minute and a standard deviation of o = 12.5 beats per minute. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. The probability is (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? O A. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. O B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. O D. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.