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 =270 days and standard deviation =26 days. (a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randomly selected pregnancy lasts less than 262 days is approximately nothing. (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 262 days or less? The probability that the mean of a a random sample of 19 pregnancies is less than 262 days is approximately nothing. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 53 pregnancies has a mean gestation period of 262 days or less? The probability that the mean of a a random sample of 53 pregnancies is less than 262 days is approximately nothing.

Explanation / Answer

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean =270 days and standard deviation =26 days.

(a) What is the probability that a randomly selected pregnancy lasts less than 262 days? The probability that a randomly selected pregnancy lasts less than 262 days is approximately nothing. (Round to four decimal places as needed.)

z value for 262, z=(262-270)/26 = -0.31

P( x < 262) = P( z < -0.31)

= 0.3783

(b) What is the probability that a random sample of 19 pregnancies has a mean gestation period of 262 days or less? The probability that the mean of a a random sample of 19 pregnancies is less than 262 days is approximately nothing. (Round to four decimal places as needed.)

Standard error = sd/sqrt(n) =26/sqrt(19) =5.9648

z value for 262, z=(262-270)/ 5.9648= -1.34

P( mean x < 262) = P( z < -1.34) =

=0.0901

(c) What is the probability that a random sample of 53 pregnancies has a mean gestation period of 262 days or less? The probability that the mean of a a random sample of 53 pregnancies is less than 262 days is approximately nothing.

Standard error = sd/sqrt(n) =26/sqrt(53) =3.5714

z value for 262, z=(262-270)/ 3.5714= -2.24

P( mean x < 262) = P( z < -2.24)

= 0.0125

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