Question

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.

Answer #1

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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