Find the indicated probability or percentage for the normally distributed variable.
-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 at least 300 days?
A)0.0166
B)0.0179
C)0.4834
D)0.9834

Question

Find the indicated probability or percentage for the normally distributed variable.
-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 at least 300 days? 
A)0.0166
B)0.0179
C)0.4834
D)0.9834

Quizplus · Accepted Answer

To find the probability that a pregnancy lasts at least 300 days, we calculate the z-score for 300 days using the formula $z = \frac{x - \mu}{\sigma}$, where $x$ is 300 days, $\mu$ is the mean (268 days), and $\sigma$ is the standard deviation (15 days). This gives us $z = \frac{300 - 268}{15} = \frac{32}{15} \approx 2.13$. Looking up this z-score in a standard normal distribution table or using a calculator, we find the probability of being above this z-score is approximately 0.0166, indicating a very low probability of a pregnancy lasting at least 300 days.

Find the Indicated Probability or Percentage for the Normally Distributed