Question

chapter 3 quiz - numerical descriptions of data
10 points possible answered: 7/11
question 8
the lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 16 days.
in what range would we expect to find the middle 68% of most lengths of pregnancies? round the answer to one decimal place.
between and days

Explanation:

Step1: Recall the empirical rule for normal distribution

For a normal - distributed data, about 68% of the data lies within 1 standard deviation of the mean. The formula for the lower bound $L$ and upper - bound $U$ of the range is $L=\mu - \sigma$ and $U=\mu+\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Identify the values of $\mu$ and $\sigma$

Given that $\mu = 267$ days and $\sigma = 16$ days.

Step3: Calculate the lower bound

$L=\mu-\sigma=267 - 16=251.0$

Step4: Calculate the upper bound

$U=\mu+\sigma=267 + 16=283.0$

Answer:

251.0, 283.0