Sample Size (n) = 15
Samples: 11, 9, 8, 10, 10, 9, 7, 11, 11, 7, 6, 9, 10, 8, 10
Standard Deviation (σ) = 1.5 mins
Mean = 9.1
Normally Distributed
Let's go ahead and solve now the confidence interval. Here are the steps.
1. Subtract the confidence interval from 1 and then divide the result by two.
[tex]\frac{1-0.90}{2}=\frac{.10}{2}=0.05[/tex]2. Subtract the result (0.05) from 1 and then look up the area in the z-distribution.
[tex]\begin{gathered} 1-0.05=0.95 \\ \end{gathered}[/tex]Looking at the z-table, the z-score that has a value of 0.95 is 1.645.
3. Use this formula and apply the given values that we got (z-value, sample size, and standard deviation).
[tex]\begin{gathered} =z\times\frac{\sigma}{\sqrt[]{n}} \\ =1.645\times\frac{1.5}{\sqrt[]{15}} \\ =1.645\times0.3872983346 \\ =0.6371 \end{gathered}[/tex]4. We will add and subtract the resulting value in number 3 to the mean of our sample. The mean given is 9.1
[tex]\begin{gathered} 9.1-0.6371=8.46\approx8.5 \\ 9.1+0.6371=9.74\approx9.7 \end{gathered}[/tex]Therefore, the confidence interval is (8.5, 9.7). It is Option 1.
