Question

19. Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 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 70 beats per minute and 78 beats per minute.

The probability is _____

​(Round to four decimal places as​ needed.)

b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 70 beats per 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), even though the sample size does not exceed​ 30?

A.Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample 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 of sample 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 capacity is 2310 lb -15 passengers. ​ So, 15 adult male passengers can have a mean weight of up to 2310 divided by 15 equals 154 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 154 lb.​ (Assume that weights of males are normally distributed with a mean of 163 lb and a standard deviation of 31 lb​.) 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 people will exceed the elevator capacity.

B.Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.

C.Yes, 15 randomly selected people will always be under the weight limit.

D.No, 15 randomly selected people will never be under the weight limit.

Answer 1