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Quz.Quz6-Chapter 8 This Question: 1 pt Submit Q Statist 2 of 5 This Quiz: 5 pts poss ses Home Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean (a) What is the probability that a randomly selected pregnancy lasts less than 227 days? The probability that a randomly selected pregnancy lasts less than 227 days is approximately (Round to four decimal places as needed.) (b) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 227 days or less? The probability that the mean of a a random sample of 17 pregnancies is less than 227 days is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 44 pregnancies has a mean gestation period of 227 days or less? The probability that the mean of a a random sample of 44 pregnancies is less than 227 days is approximately(Round to four decimal places as needed.) ơ-22 days. Contents nch d Solutions nal Resources ork & Tests lan ook edia Library

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Answer #1

Let X denotes the length of pregnancy of a randomly selecting animal.

X ~ Normal(235, 222)

a) Now,

X-227 235-227 . הפ) _ p( ) = P(Z < -0.363636) = o(-0.363636) 0.358065

b) Let Y denotes the length of pregnancy of a randomly selecting group of 17 people.

22- Y Normal(235,- 17 or ~ Normal (235.5335782)

Now,

y-235 / 227-235) = P(Z < -1.49931) Pl < -5.33578 Ply < 227)-Pl 5.33578 < 5335 Φ(-1.49931) 0.0668966

c) Let X denotes the length of pregnancy of a randomly selecting group of 44 people.

Y Normal (235. _) or Y ~ Normal (235, 3.316622)

Now,

X-235 一一166.- P(X < 227) = P( Φ(-2.41209) = 0.0079307 ) = P(Z < -2.41209) . 3.31662 0.007930 .31662 〈 2- 235

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