Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=253 days and standard deviation σ=17 days. Complete parts (a) through (f) below.

(a) What is the probability that a randomly selected pregnancy lasts less than 247 days?

The probability that a randomly selected pregnancy lasts less than 247 days is approximately: ______

(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 less than _____days.

B.

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

______ pregnancies to last more than _____days.

C.

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

_____ pregnancies to last exactly _____days.

(b) Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of overbar x is (Normal, not normal ..ect) with μx =____

and σx =______

(Round to four decimal places as needed.)

(c) What is the probability that a random sample of 20 pregnancies has a mean gestation period of 247 days or less?

The probability that the mean of a random sample of 20 pregnancies is less than 247days is approximately: _____

(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 = 20 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of exactly 247days.

B.

If 100 independent random samples of size n = 20 pregnancies were obtained from this population, we would expect _____sample(s) to have a sample mean of 247 days or less.

C.

If 100 independent random samples of size n = 20 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of 247days or more.

(d) What is the probability that a random sample of 32 pregnancies has a mean gestation period of

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=253 days and standard deviation σ=17 days. Complete parts (a) through (f) below.

(a) What is the probability that a randomly selected pregnancy lasts less than 247 days?

The probability that a randomly selected pregnancy lasts less than 247 days is approximately: ______

(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 less than _____days.

B.

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

______ pregnancies to last more than _____days.

C.

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

_____ pregnancies to last exactly _____days.

(b) Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of overbar x is (Normal, not normal ..ect) with μx =____

and σx =______

(Round to four decimal places as needed.)

(c) What is the probability that a random sample of 20 pregnancies has a mean gestation period of 247 days or less?

The probability that the mean of a random sample of 20 pregnancies is less than 247days is approximate: _____

(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 = 20 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of exactly 247days.

B.

If 100 independent random samples of size n = 20 pregnancies were obtained from this population, we would expect _____sample(s) to have a sample mean of 247 days or less.

C.

If 100 independent random samples of size n = 20 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of 247days or more.

(d) What is the probability that a random sample of 32 pregnancies has a mean gestation period of

247 days or less?

The probability that the mean of a random sample of 32 pregnancies is less than 247days is approximately _____.

(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 = 32 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of 247days or more.

B.

If 100 independent random samples of size n = 32 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 247days or less.

C.

If 100 independent random samples of size n = 32 pregnancies were obtained from this    population, we would expect _____ sample(s) to have a sample mean of exactly 247days.

(e) What might you conclude if a random sample of 32 pregnancies resulted in a mean gestation period of

247days or less?

This result would be (usual, un-usual …ect.) so the sample likely came from a population whose mean gestation period is (Equal, less than, more than ..ect) to 128 days.

(f) What is the probability a random sample of size 18 will have a mean gestation period within 8 days of the mean?

The probability that a random sample of size 18 will have a mean gestation period within 8 days of the mean is _____

(Round to four decimal places as needed.)

days or less?

The probability that the mean of a random sample of 32 pregnancies is less than 247days is approximately _____.

(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 = 32 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of 247days or more.

B.

If 100 independent random samples of size n = 32 pregnancies were obtained from this population, we would expect ____ sample(s) to have a sample mean of 247days or less.

C.

If 100 independent random samples of size n = 32 pregnancies were obtained from this population, we would expect _____ sample(s) to have a sample mean of exactly 247days.

(e) What might you conclude if a random sample of 32 pregnancies resulted in a mean gestation period of

247 days or less?

This result would be (usual, un-usual …ect.) so the sample likely came from a population whose mean gestation period is (Equal, less than, more than ..ect) to 128 days.

(f) What is the probability of a random sample of size 18 will have a mean gestation period within 8 days of the mean?

The probability that a random sample of size 18 will have a mean gestation period within 8 days of the mean is _____

(Round to four decimal places as needed.)

Answer 1

Let X is a random variable shows the length of pregnancy.

Here X has normal distribution with following parameters:

(A)

The z-score for X = 247 is

The probability that pregnancy last less than 247 days is

P(X < 247) = P(z < -0.35) = 0.3632

The expected pregnancies in 100 is 100 *0.3632= 36.32

Correct option:

A.

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

36 pregnancies to last less than 247 days.

(b)

The sampling distribution of sample mean will be normal distribution with mean

and standard deviation

(c)

The z-score for is

The required probability is

The expected number of pregnancies: 100 * 0.0571 = 5.71

Correct option:

B. If 100 independent random samples of size n = 20 pregnancies were obtained from this population, we would expect 6 sample(s) to have a sample mean of 247 days or less.

(d)

The standard deviation

The z-score for is

The required probability is

The expected number of pregnancies: 100 * 0.0228= 2.28

B.

If 100 independent random samples of size n = 32 pregnancies were obtained from this population, we would expect 2 sample(s) to have a sample mean of 247days or less.