Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 238 days and standard deviation sigma equals 14 days. What is the probability that a randomly selected pregnancy lasts less than 233 ​days?

Answer 1

Answer:

Probability that a randomly selected pregnancy lasts less than 233 ​days is 0.3594.

Step-by-step explanation:

We are given that the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 238 days and standard deviation sigma equals 14 days.

Let X = lengths of the pregnancies of a certain animal

So, X ~ Normal($\mu=238,\sigma^{2} =14^{2}$)

The z score probability distribution for normal distribution is given by;

                         Z  =  $\frac{X-\mu}{\sigma}$  ~ N(0,1)

where, $\mu$ = population mean = 238 days

           $\sigma$ = standard deviation = 14 days

Now, the probability that a randomly selected pregnancy lasts less than 233 ​days is given by = P(X < 233 days)

   P(X < 233 days) = P( $\frac{X-\mu}{\sigma}$ < $\frac{233-238}{14}$ ) = P(Z < -0.36) = 1 - P(Z $\leq$ 0.36)

                                                              = 1 - 0.6406 = 0.3594

The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.