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

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

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 =
`(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(
`(X-\mu)/(\sigma)` <
`(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.