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 ?=180 days ?=16 days.

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

A. What is the probability that a randomly selected pregnancy lasts less than 175 ?days?

B. Suppose a random sample of 20 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies. The sampling distriution (is skewed in what way?) with mu=? and standard deviation= ?

C. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 175 days or? less?

D. What is the probability that a random sample of 59 pregnancies has a mean gestation period of 175 days or? less?

E. ) What might you conclude if a random sample of 59 pregnancies resulted in a mean gestation period of 175 days or? less? This result would be (expected or unusual) so the sample likely came from a population whose mean gestation period is (greater than, less than, or equal to)

F. What is the probability a random sample of size 20 will have a mean gestation period within 12 days of the? mean?

Explanation / Answer

Ans:

Given that

?=180 days ?=16 days

a)

z=(175-180)/16=-0.3125

P(z<-0.3125)=0.3773

b)Normal distribution with mean=180 and standard deviation=16/sqrt(20)=3.578

c)

z=(175-180)/3.578=-1.398

P(z<=-1.398)=0.0811

d)

z=(175-180)/(16/sqrt(59))

z=-2.40

P(z<-2.40)=0.0082

e)unusual,so the sample likely came from a population whose mean gestation period is less than

f)z=+/-12/3.578=+/-3.354

P(-3.354<z<3.354)=0.9996-0.0004=0.9992

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