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?

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([tex]\mu=238,\sigma^{2} =14^{2}[/tex])

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

Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 238 days

[tex]\sigma[/tex] = 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( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{233-238}{14}[/tex] ) = P(Z < -0.36) = 1 - P(Z [tex]\leq[/tex] 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.

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?

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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?