Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 131 days   μ=131 days and standard deviation sigma equals 8 days   σ=8 days

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Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 131 days

 

μ=131 days and standard deviation sigma equals 8 days

 

σ=8 days. Complete parts? (a) through? (f) below.

?(a) What is the probability that a randomly selected pregnancy lasts less than 128

 

128 ?days?

The probability that a randomly selected pregnancy lasts less than 128

 

128 days is approximately

0.352

 

0.352. ?(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

35

 

35 pregnancies to last less than 128

 

128 days.

Your answer is correct.

B.

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

nothing

 

pregnancies to last more than 128

 

128 days.

C.

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

nothing

 

pregnancies to last exactly 128

 

128 days.

?(b) Suppose a random sample of 19

 

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

The sampling distribution of x overbar

 

x is normal

with mu Subscript x overbar

 

μxequals

 

=

131

 

131 and sigma Subscript x overbar

 

σxequals

 

=

nothing

 

.

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