Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean
μ=293 days
and standard deviation
σ=21 days.
Complete parts (a) through (f) below.
(a) What is the probability that a randomly selected pregnancy lasts less than
285
days?
The probability that a randomly selected pregnancy lasts less than
285
days is approximately
. 3516.3516.
(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
pregnancies to last exactly
285
days.
B.
If 100 pregnant individuals were selected independently from this population, we would expect
pregnancies to last more than
285
days.
C.
If 100 pregnant individuals were selected independently from this population, we would expect
3535
pregnancies to last less than
285
days.
(b) Suppose a random sample of
18
pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
The sampling distribution of
x
is
normal
with
μx=293293
and
σx=4.94974.9497.
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of
18
pregnancies has a mean gestation period of
285
days or less?
The probability that the mean of a random sample of
18
pregnancies is less than
285
days is approximately
. 0530.0530.
(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 independent random samples of size
n=18
pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of
285
days or more.
B.
If 100 independent random samples of size
n=18
pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of
285
days or less.
C.
If 100 independent random samples of size
n=18
pregnancies were obtained from this population, we would expect
sample(s) to have a sample mean of exactly
285
days.