Answer
μ is between 0.7282 and 1.1482. 1.6 is more than the upper bound of the interval, hence the radiation must be 1.6 or less.
Work Step by Step
The mean can be counted by summing all the data and dividing it by the number of data: $\frac{0.38+0.55+...+1.46}{11}=0.9382.$
Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(0.38-0.9382)^2+...+(1.46-0.9382)^2}{10}}=0.4229.$
α=1−0.9=0.1. σ is 0.4229, hence we use the z-distribution with df=sample size−1=11−1=10 in the table. $z_{\alpha/2}=z_{0.05}=1.645.$ Margin of error:$z_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.645\cdot\frac{0.4229}{\sqrt{11}}=0-21.$ Hence the confidence interval:μ is between 0.9382-0.21=0.7282 and 0.9382+0.21=1.1482. 1.6 is more than the upper bound of the interval, hence the radiation must be 1.6 or less.