Question

Suppose that the lengths of human pregnancies are normally distributed with a mean of 267 days and a standard deviation of 17 days. Complete the following statements. (a) Approximately ? of pregnancies have lengths between 216 days and 318 days. (b) Approximately 95% of pregnancies have lengths between days and 1 days Х ?

Answer 1

To determine the probabilities, we need to find the z-scores corresponding to the given values and then use the z-table. (a) Approximately 0.13% of pregnancies have lengths between 216 days and 318 days. (b) Approximately 95% of pregnancies have lengths between 239 days and 295 days.

Step-by-step explanation:

To determine the probabilities, we need to find the z-scores corresponding to the given values and then use the z-table.

(a) To find the probability that a pregnancy length is between 216 days and 318 days:

Find the z-score for 216 days: z = (216 - 267) / 17 = -3

Find the z-score for 318 days: z = (318 - 267) / 17 = 3

Using the z-table, we find that approximately 0.0013 (or 0.13%) of pregnancies have lengths between 216 days and 318 days.

(b) To find the range of days where approximately 95% of pregnancies fall:

Find the z-score for the lower end: z = (x - 267) / 17

Using the z-table, the z-score for the lower end corresponds to 0.025.

Find the z-score for the upper end: z = (x - 267) / 17

Using the z-table, the z-score for the upper end corresponds to 0.975.

Let x be the lower end:

0.025 = (x - 267) / 17

Solving for x, we get x ≈ 238.95.

Let x be the upper end:

0.975 = (x - 267) / 17

Solving for x, we get x ≈ 295.05.

Therefore, approximately 95% of pregnancies have lengths between 239 days and 295 days.