Chapter 7 - Confidence Intervals and Sample - 7-1 Confidence Intervals for the Mean When σ Is Known - Exercises 7-1 - Page 379: 14

$2.6\lt\mu\lt3.1$

1. The mean of the data set can be found as $\bar X=2.819$ 2. At the 99% confidence, the critical z-value is $z_{\alpha/2}=2.575$ 3. Given $\sigma=0.62,n=36$, the error of estimation can be found as $E=2.575\times\frac{0.62}{\sqrt {36}}=0.266$ 4. the interval of the mean can be found as $\bar X−E\lt\mu\lt\bar X+E$ which gives $2.6\lt\mu\lt3.1$