Question

What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?

Answer 1

In order to calculate the confidence interval, we can use the formula below:

`CI=\mu\pm z\cdot(\sigma)/(√(n))`

For an interval with a confidence of 99%, we need to use z = 2.576.

Then, using a mean of 85.6, a standard deviation of 2.9 and a sample size of 52, we have:

`\begin{gathered} CI=85.6\pm2.576\cdot(2.9)/(√(52))\\ \\ CI=85.6\pm2.576\cdot0.4021576\\ \\ CI=85.6\pm1.036\\ \\ CI=(84.564,86.636) \end{gathered}`