19. Assume that females have pulse rates that are normallydistributed with a mean of mu equals 74.0 beats per minute and astandard deviation of sigma equals 12.5 beats per minute. Completeparts​ (a) through​ (c) below.
a. If 1 adult female is randomly​ selected, find the probabilitythat her pulse rate is between 70 beats per minute and 78 beats perminute.
The probability is _____
​(Round to four decimal places as​ needed.)
b. If 4 adult females are randomly​ selected, find theprobability that they have pulse rates with a mean between 70 beatsper minute and 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), eventhough the sample size does not exceed​ 30?
A.Since the original population has a normal​ distribution, thedistribution of sample means is a normal distribution for anysample size.
B.Since the distribution is of​ individuals, not sample​ means,the distribution is a normal distribution for any sample size.
C.Since the mean pulse rate exceeds​ 30, the distribution ofsample means is a normal distribution for any sample size.
D.Since the distribution is of sample​ means, not​ individuals,the distribution is a normal distribution for any sample size.
20. An elevator has a placard stating that the maximum capacityis 2310 lb -15 passengers. ​ So, 15 adult male passengers can havea mean weight of up to 2310 divided by 15 equals 154 pounds. If theelevator is loaded with 15 adult male​ passengers, find theprobability that it is overloaded because they have a mean weightgreater than 154 lb.​ (Assume that weights of males are normallydistributed with a mean of 163 lb and a standard deviation of 31lb​.) Does this elevator appear to be​ safe?
The probability the elevator is overloaded is_____
​(Round to four decimal places as​ needed.)
Does this elevator appear to be​ safe?
A.No, there is a good chance that 15 randomly selected peoplewill exceed the elevator capacity.
B.Yes, there is a good chance that 15 randomly selected peoplewill not exceed the elevator capacity.
C.Yes, 15 randomly selected people will always be under theweight limit.
D.No, 15 randomly selected people will never be under the weightlimit.
