The duration (in days) of human pregnancies follows approximately the N(266, 16) distribution. How many days would a human pregnancy need to last to be among the top 10% of all pregnancy durations?
A)239.7 days
B)245.5 days
C)286.5 days
D)292.3 days

Question

Quizplus · Accepted Answer

We need to find the duration of pregnancy that corresponds to the top 10% of all pregnancy durations.

To do this, we need to find the z-score that corresponds to the 90th percentile.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 90th percentile is approximately 1.28.

We can then use the formula for standardizing a normal distribution to find the corresponding duration:

z = (x - μ) / σ

1.28 = (x - 266) / 16

Solving for x, we get:

x = 286.5

Thus, a human pregnancy would need to last approximately 286.5 days to be among the top 10% of all pregnancy durations.

Therefore, the correct answer is (C).

The Duration (In Days) of Human Pregnancies Follows Approximately the N(266