Suppose the lengths of the pregnancies of a certain animal are approximately nor

Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean -299 days and standard deviation = 24 days (a) What is the probability that a randomly selected pregnancy lasts less than 290 days? The probability that a randomly selected pregnancy lasts less than 290 days is approximately. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 290 days or less? The probability that the mean of a a random sample of 19 pregnancies is less than 290 days is approximately(Round to four decimal places as needed.) (c) What is the probability that a random sample of 45 pregnancies has a mean gestation period of 290 days or less? probability that the meano ess than 290 days is approximately (Round to four decimal places a

Explanation / Answer

Sol:

mean=299

sd=24

SolutionA:

P(X<290)

z=x-mean/sd

=290-299/24

=-9/24

z=-0.375

P(Z<-0.375)

=1-P(Z<0.375)

=1-0.648

=0.352

ANSWER:0.352

SOLUTIONB:

n=19

P(X<290)

z=290-299/24/sqrt(19)

=-1.635

P(Z<-1.635)

=1-P(Z<1.635)

=1-0.9495

=0.0505

ANSWER:0.0505

Solutionc:

n=45

P(X<290)

Z=290-299/24/sqrt(45)

=-2.516

P(Z<-2.516)

=1-P(Z<2.516)

=1-0.9941

=0.0059

ANSWER:0.0059

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