Question

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts more than 300 days? a. Draw the sketch and shade the appropriate area under the curve b. Solve for the Z-score c. Find the probability of a pregnancy lasting more than 300 days

Answer 1

To find the probability that a pregnancy lasts more than 300 days, draw a normal distribution curve, calculate the Z-score which is approximately 2.13, and then find the probability associated with that Z-score, which will be small due to the Z-score's position on the curve.

Step-by-step explanation:

The probability that a pregnancy lasts more than 300 days can be found using the Z-score and the standard normal distribution.

Step 1: Draw the sketch and shade the appropriate area under the curve

First, we draw a normal distribution curve with a mean (μ) of 268 days and a standard deviation (σ) of 15 days. We then shade the area to the right of the 300 days mark, representing pregnancies that last more than 300 days.

Step 2: Solve for the Z-score

We calculate the Z-score using the formula:

Z = (X - μ) / σ

Where X is 300 days.

Z = (300 - 268) / 15 ≈ 2.13

Step 3: Find the probability

To find the probability of a pregnancy lasting more than 300 days, we look up the Z-score in a standard normal distribution table or use a calculator designed for this purpose, which will give us the area to the right of the Z-score. Since the Z-score of 2.13 is far to the right of the mean on the distribution curve, the probability is relatively small.