entral Theorem
Question 4, 8.1.19-T
HW Score: $59.5 \%, 59.5$ of 100 points
Part 1 ot 9
Points: 0 of 20
The length of human pregnancles is approximately normal with mean $\mu=266$ days and standard deviation $\sigma=16$ days. Complete parts (a) through (f).
(a) What is the probability that a randomly selected pregnancy lasts less than 260 days?

The probability that a randomly selected pregnancy lasts less than 260 days is approximately $\square$.
(Round to four decimal places as needed.)

Step 1 ：The problem is asking for the probability that a randomly selected pregnancy lasts less than 260 days. This is a problem of normal distribution. We know that the mean (μ) is 266 days and the standard deviation (σ) is 16 days.

Step 2 ：We can use the Z-score formula to find the Z-score for 260 days, which is \((X - μ) / σ\).

Step 3 ：Substituting the given values into the formula, we get \(Z = (260 - 266) / 16 = -0.375\).

Step 4 ：We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability that a randomly selected pregnancy lasts less than 260 days.

Step 5 ：The probability is approximately 0.3538.

Step 6 ：Final Answer: The probability that a randomly selected pregnancy lasts less than 260 days is approximately \(\boxed{0.3538}\).