A boat capsized and sank in a lake. Based on an assumption of amean weight of
130130
​lb, the boat was rated to carry
7070
passengers​ (so the load limit was
9 comma 1009,100
​lb). After the boat​ sank, the assumed mean weight for similarboats was changed from
130130
lb to
172172
lb. Complete parts a and b below.
a. Assume that a similar boat is loaded with
7070
​passengers, and assume that the weights of people are normallydistributed with a mean of
175.6175.6
lb and a standard deviation of
40.840.8
lb. Find the probability that the boat is overloaded becausethe
7070
passengers have a mean weight greater than
130130
lb.The probability is
nothing.
​(Round to four decimal places as​ needed.)
b. The boat was later rated to carry only
1717
​passengers, and the load limit was changed to
2 comma 9242,924
lb. Find the probability that the boat is overloaded because themean weight of the passengers is greater than
172172
​(so that their total weight is greater than the maximumcapacity of
2 comma 9242,924
​lb).The probability is
nothing.
​(Round to four decimal places as​ needed.)
Do the new ratings appear to be safe when the boat is loadedwith
1717
​passengers? Choose the correct answer below.
A.Because there is a high probability of​ overloading, the newratings do not appear to be safe when the boat is loaded with
1717
passengers.
B.
Because the probability of overloading is lower with the newratings than with the old​ ratings, the new ratings appear to besafe.
C.Because there is a high probability of​ overloading, the newratings appear to be safe when the boat is loaded with
1717
passengers.
D.Because
175.6175.6
is greater than
172172​,
the new ratings do not appear to be safe when the boat is loadedwith
1717
passengers.
___________________________________________________________________________________________________________________
Assume that females have pulse rates that are normallydistributed with a mean of
mu equals 75.0μ=75.0
beats per minute and a standard deviation of
sigma equals 12.5σ=12.5
beats per minute. Complete parts​ (a) through​ (c) below.
a. If 1 adult female is randomly​ selected, find the probabilitythat her pulse rate is between
6868
beats per minute and
8282
beats per minute.The probability is
0.42460.4246.
​(Round to four decimal places as​ needed.)
b. If
1616
adult females are randomly​ selected, find the probability thatthey have pulse rates with a mean between
6868
beats per minute and
8282
beats per minute.The probability is
00.
​(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 distribution is of​ individuals, not sample​ means,the distribution is a normal distribution for any sample size.
B.
Since the distribution is of sample​ means, not​ individuals,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 original population has a normal​ distribution, thedistribution of sample means is a normal distribution for anysample size.
