Question

The pregnancy duration in days for a population of new mother can be approximated by a normal distribution, with a mean of 267 days and a standard deviation of 8 days. a. what is the minimum pregnancy durations that can be in the top 9% of pregnancy durations?

A) 275 days
B) 277 days
C) 263 days
D) 257 days

Answer 1

To find the minimum pregnancy duration in the top 9% of pregnancy durations, calculate the z-score associated with the 9th percentile and use it to find the corresponding duration in days.

Step-by-step explanation:

To find the minimum pregnancy duration that can be in the top 9% of pregnancy durations, we need to find the z-score associated with the 9th percentile. The z-score can be calculated using the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have:

x = z * σ + μ.

For the top 9% of the distribution, the corresponding percentile is 91%. Using a standard normal table, the z-score associated with the 91st percentile is approximately 1.34.

Plugging in the values, we have:

x = 1.34 * 8 + 267 = 277.72.

Since pregnancy durations are typically considered in whole days, the minimum pregnancy duration that can be in the top 9% is 278 days.