Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean...

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean

mu equals 147 daysμ=147 days

and standard deviation

sigma equals 12 daysσ=12 days.

Complete parts​ (a) through​ (f) below.Click here to view the standard normal distribution table (page 1).

​(a) What is the probability that a randomly selected pregnancy lasts less than

143143

​days?The probability that a randomly selected pregnancy lasts less than

143143

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 this​ population, we would expect

nothing

pregnancies to last more than

143143

days.

B.If 100 pregnant individuals were selected independently from this​ population, we would expect

nothing

pregnancies to last less than

143143

days.

C.If 100 pregnant individuals were selected independently from this​ population, we would expect

nothing

pregnancies to last exactly

143143

days.​(b) Suppose a random sample of

1919

pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.The sampling distribution of

x overbarx

is

normal

skewed right

skewed left

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

1919

pregnancies has a mean gestation period of

143143

days or​ less?The probability that the mean of a random sample of

1919

pregnancies is less than

143143

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=1919

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

143143

days or more.

B.If 100 independent random samples of size

nequals=1919

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

143143

days or less.

C.If 100 independent random samples of size

nequals=1919

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of exactly

143143

days.​(d) What is the probability that a random sample of

4848

pregnancies has a mean gestation period of

143143

days or​ less?The probability that the mean of a random sample of

4848

pregnancies is less than

143143

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=4848

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of exactly

143143

days.

B.If 100 independent random samples of size

nequals=4848

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

143143

days or less.

C.If 100 independent random samples of size

nequals=4848

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

143143

days or more.​(e) What might you conclude if a random sample of

4848

pregnancies resulted in a mean gestation period of

143143

days or​ less?This result would be

unusual,

expected,

so the sample likely came from a population whose mean gestation period is

less than

equal to

greater than

147147

days.​(f) What is the probability a random sample of size

1919

will have a mean gestation period within

88

days of the​ mean?The probability that a random sample of size

1919

will have a mean gestation period within

88

days of the mean is

nothing.

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