Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 213 daysμ=213 days and standard deviation sigma equals 19 daysσ=19 days. Complete parts (a) through (f) below.
(a) What is the probability that a randomly selected pregnancy lasts less than 206 days?
The probability that a randomly selected pregnancy lasts less than 206 days is approximately
nothing. (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 thispopulation, we would expect
nothing pregnancies to last exactly 206 days.
B.
If 100 pregnant individuals were selected independently from thispopulation, we would expect
nothing pregnancies to last less than 206 days.
C.
If 100 pregnant individuals were selected independently from thispopulation, we would expect
nothing pregnancies to last more than 206 days.
(b) Suppose a random sample of 21 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
The sampling distribution of x overbarx is
▼
skewed left
skewed right
normal
with mu Subscript x overbarμxequals=
nothing and sigma Subscript x overbarσxequals=
nothing.
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 21 pregnancies has a mean gestation period of 206 days or less?
The probability that the mean of a random sample of 21 pregnancies is less than 206 days is approximately
nothing.
(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 nequals=21 pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of 206days or less.
B.
If 100 independent random samples of size nequals=21pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of exactly 206 days.
C.
If 100 independent random samples of size nequals=21 pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of 206 days or more.
(d) What is the probability that a random sample of 32 pregnancies has a mean gestation period of 206 days or less?
The probability that the mean of a random sample of 32 pregnancies is less than 206 days is approximately
nothing.
(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 nequals=32 pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of exactly 206 days.
B.
If 100 independent random samples of size nequals=32 pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of 206 days or more.
C.
If 100 independent random samples of size nequals=32pregnancies were obtained from this population, we would expect
nothing sample(s) to have a sample mean of 206 days or less.
(e) What might you conclude if a random sample of 32 pregnancies resulted in a mean gestation period of 206 days or less?
This result would be
▼
unusual,
expected,
so the sample likely came from a population whose mean gestation period is
▼
equal to
less than
greater than
213 days.
(f) What is the probability a random sample of size 17 will have a mean gestation period within 12 days of the mean?
The probability that a random sample of size 17 will have a mean gestation period within 12 days of the mean is
nothing.
(Round to four decimal places as needed.)