Question

1.Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 214 days

μ=214 days and standard deviation sigma equals 19 days

σ=19 days. Complete parts​ (a) through​ (f) below.

​(a) What is the probability that a randomly selected pregnancy lasts less than 208 ​days?

2.The probability that a randomly selected pregnancy lasts less than 208 days is approximately .3761. ​(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.)

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

38 pregnancies to last less than 208 days.

​(b) Suppose a random sample of 22 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of x is ______

with mu Subscript x = _______

and sigma Subscript x = _______

.

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