Question

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

mu equals μ=197 daysand standard deviation sigma equals sσ=14 days. Complete parts​ (a) through​ (f) below.

​(a) What is the probability that a randomly selected pregnancy lasts less than 192 ​days?

The probability that a randomly selected pregnancy lasts less than 192 days is approximately 0.3604 ​(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.)

B.If 100 pregnant individuals were selected independently from this​ population, we would expect 36 pregnancies to last less than

192 days.

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

The sampling distribution of x overbarx is normal with mu Subscript x overbar μx equals=197 and sigma Subscript x overbarσxequals=3.1305 ​(Round to four decimal places as​needed.)

What is the probability that a random sample of 20 pregnancies has a mean gestation period of 192 days or​ less?

The probability that the mean of a random sample of 20 pregnancies is less than 192 days is approximately 0.0551. ​(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=20 pregnancies were obtained from this​ population, we would expect 6 ​sample(s) to have a sample mean of 192 days or less.

(d) What is the probability that a random sample of 48 pregnancies has a mean gestation period of 192 days or​ less?

The probability that the mean of a random sample of 48 pregnancies is less than 192 days is approximately 0.0067. ​(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.)

C.If 100 independent random samples of size n equals= 48 pregnancies were obtained from this​ population, we would expect 1 sample(s) to have a sample mean of 192 days or less.

​(e) What might you conclude if a random sample of 48 pregnancies resulted in a mean gestation period of 192 days or​less?

This result would be Unusual ▼  so the sample likely came from a population whose mean gestation period is Less than ▼ 197 days.

NOTE: I need to resolve this last question #f and need to know how to do the steps also. Thanks!

(f) What is the probability a random sample of size 19  will have a mean gestation period within 10  days of the​ mean?

The probability that a random sample of size 19  will have a mean gestation period within 10  days of the mean is _________. ​(Round to four decimal places as​ needed.)

I know I have to take =14/sqrt(19) which gives me 3.21182027. I have to divide 10 days by 2 which gives me 5. This is where I get confused .........

Answer 1

(f) What is the probability a random sample of size 19  will have a mean gestation period within 10  days of the​ mean?

• The probability that a random sample of size 19  will have a mean gestation period within 10  days of the mean is _________. ​(Round to four decimal places as​ needed.)

Answer:- Here margin of error (ME) is 10, so you do not need to divide 10 by 2.

           Now,

                     

So,

So,

The probability that a random sample of size 19  will have a mean gestation period within 10  days of the mean is 0.9991.

Feel free to ask any query about this through comments! Thank you so much!