The gestation period of humans follows an approximately normal distribution with a mean of 266 days and a standard deviation of 16 days.Find the probability that a gestation period is between 260 and 276 days.Round to four decimal places.
A)0.1901
B)0.3802
C)0.2851
D)0.0950

Question

Quizplus · Accepted Answer

To find the probability that a gestation period is between 260 and 276 days, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 260$, $Z = \frac{260 - 266}{16} = -0.375$. For $X = 276$, $Z = \frac{276 - 266}{16} = 0.625$. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities: $P(Z < 0.625) - P(Z < -0.375)$. This difference gives us the probability of a gestation period being between 260 and 276 days, which is approximately 0.3802.

The Gestation Period of Humans Follows an Approximately Normal Distribution