The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days.
A)0.0166
B)0.9834
C)0.2375
D)0.3189

Question

Quizplus · Accepted Answer

To find the probability of a pregnancy lasting more than 300 days, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (300 days), μ is the mean (268 days), and σ is the standard deviation (15 days). Plugging in the values, we get Z = (300 - 268) / 15 = 32 / 15 ≈ 2.13. Looking up 2.13 in the standard normal distribution table gives us the area to the left of Z, which is approximately 0.9834. Since we want the area to the right (the probability of lasting more than 300 days), we subtract this from 1, giving 1 - 0.9834 = 0.0166.

The Lengths of Pregnancies of Humans Are Normally Distributed with a Mean