Question

usparteslid 194526222& centerwinsyes Introduction To Statistics (W118-19 Mat 102 JA) Quiz: Quiz 6 - Chapter 8 his Question: 1 pt 2 of 5 the lengths of the pregnancies of a certain animal are approximately normally distributed with mean-240 day and standard deviation ơ 21 days. (a) What is the probability that a randomly selected pregnancy lasts less than 233 days? The probability that a randomly selected pregnancy lasts less than 233 days is approximately Round to four decimal places as needed) (b) What is the probability that a random sample of 14 pregnancies has a mean gestation The probability that the mean of a a random sample of 14 pregnancies is less than 233 days is approximately (Round to four decimal places as (c) What is the probability that a random sample of 41 pregnancies has a mean gestation period of 233 days or less? The probability that the mean of a a random sample of 41 pregnancies is less than 233 days is approximately(Round to tour decimal places as needed) period of 233 days or less? needed.)

Answer 1

Solution:-

Mean = 240, S.D = 21

a) The probability that a randomly selected pregnancy lasts less than 233 days is 0.3695.

x = 233

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = -0.333

P(z < - 0.3333) = 0.3695

b) The probability that a random sample of 14 pregnancies has a mean gestation period of 233 days or less is 0.1056.

x = 233

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = -1.25

P(z < -1.25) = 0.1056

c) The probability that a random sample of 41 pregnancies has a mean gestation period of 233 days or less is 0.0166.

x = 233

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = -2.13

P(z < -2.13) = 0.0166