Question

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

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

mu equals 273 daysμ=273 days

and standard deviation

sigma equals 17 daysσ=17 days.

Complete parts​ (a) through​ (f) below.

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

267267

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

267267

days is approximately

. 3632.3632.

​(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

267267

days.

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

nothing

pregnancies to last exactly

267267

days.

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

nothing

pregnancies to last less than

267267

days.

Solution :

Given that ,

mean = = 273 days

standard deviation = = 17 days

a) P(x < 267) = P[(x - ) / < (267 - 273) / 17]

= P(z < -0.35)

Using z table,

= 0.3632

b) n = 100

= 100 * 0.3632 = 36.32

= 36 pregnancies.

correct option is = C

C.If 100 pregnant individuals were selected independently from this​ population, we would expect 36 pregnancies to last less than 267 days

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