Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean
mu equals 142 daysμ=142 days
and standard deviation
sigma equals 9 daysσ=9 days.
Complete parts (a) through (f) below.
(a) What is the probability that a randomly selected pregnancy lasts less than
139139
days?The probability that a randomly selected pregnancy lasts less than
139139
days is approximately
0.36940.3694.
(Round to four decimal places as needed.)
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
(Round to the nearest integer as needed.)
A.If 100 pregnant individuals were selected independently from this population, we would expect
nothing
pregnancies to last exactly
139139
days.Your answer is not correct.
B.If 100 pregnant individuals were selected independently from this population, we would expect
3737
pregnancies to last less than
139139
days.
C.If 100 pregnant individuals were selected independently from this population, we would expect
nothing
pregnancies to last more than
139139
days.(b) Suppose a random sample of
1818
pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.The sampling distribution of
x overbarx
is
normal
with
mu Subscript x overbarμxequals=142142
and
sigma Subscript x overbarσxequals=2.12132.1213.
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of
1818
pregnancies has a mean gestation period of
139139
days or less?The probability that the mean of a random sample of
1818
pregnancies is less than
139139
days is approximately
nothing.
(Round to four decimal places as needed.)
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