Question

In a random sample of 30 young bears, the average weight at the age of breeding is 312 pounds. Assuming the population ages are normally distributed with a population standard deviation is 30 pounds, use the Empirical Rule to construct a 68% confidence interval for the population average of young bears at the age of breeding. Do not round intermediate calculations. Round only the final answer to the nearest pound. Remember to enter the smaller value first, then the larger number.

Answer 1

We have that the empirical rule to construct a 68% confidence interval can be expressed with the following general rule:

$(\mu-\sigma,\mu+\sigma)$

in this case, we have the following information:

$\begin{gathered} \mu=312 \\ \sigma=30 \end{gathered}$

then, the confidence interval with 68% of confidence is:

$(312-30,312+30)=(282,342)$

therefore, the confidence interval with 68% of confidence is (282,342)