Chapter 7 - Confidence Intervals and Sample - 7-1 Confidence Intervals for the Mean When σ Is Known - Exercises 7-1 - Page 380: 22

$57.4\lt\mu\lt58.6$

Given $\bar X=58, \sigma=4.8, n=171$, at the 90% confidence, the critical z-value is $z_{\alpha/2}=1.645$ and the margin of error can be found as $E=1.645\times\frac{4.8}{\sqrt {171}}=0.604$ Thus, the interval of the true mean can be found as $\bar X-E\lt\mu\lt\bar X+E$ which gives $57.4\lt\mu\lt58.6$