Question

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

mu equals 135 daysμ=135 days

and standard deviation

sigma equals 14 daysσ=14 days.

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

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Click here to view the standard normal distribution table (page 2).

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

130130

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

130130

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

130130

days.

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

nothing

pregnancies to last less than

130130

days.

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

nothing

pregnancies to last exactly

130130

days.​(b) Suppose a random sample of

1717

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

1717

pregnancies has a mean gestation period of

130130

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

1717

pregnancies is less than

130130

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=1717

pregnancies were obtained from this​ population, we would expect

nothing

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

130130

days.

B.If 100 independent random samples of size

nequals=1717

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

130130

days or less.

C.If 100 independent random samples of size

nequals=1717

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

130130

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

5050

pregnancies has a mean gestation period of

130130

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

5050

pregnancies is less than

130130

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=5050

pregnancies were obtained from this​ population, we would expect

nothing

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

130130

days.

B.If 100 independent random samples of size

nequals=5050

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

130130

days or less.

C.If 100 independent random samples of size

nequals=5050

pregnancies were obtained from this​ population, we would expect

nothing

​sample(s) to have a sample mean of

130130

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

5050

pregnancies resulted in a mean gestation period of

130130

days or​ less?This result would be

▼

expected,

unusual,

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

▼

greater than

equal to

less than

135135

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

1717

will have a mean gestation period within

1111

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

1717

will have a mean gestation period within

1111

days of the mean is

nothing.

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

Answer 1