Question

The data in the Table are the result of a random survey of $39$national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let $X=$the number of colors on a national flag.

$\begin{array}{|cc|}\hline X& \text{Freq.}\\ 1& 1\\ 2& 7\\ 3& 18\\ 4& 7\\ 5& 6\\ \hline\end{array}$

Construct a localid="1648450905983" $95\%$confidence interval for the true mean number of colors on national flags.

Fill in the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean.

Short answer

We know that the mean number of colors on national flags was $3.26$, lower and upper limits of the confidence interval were $2.93$ and $3.59$, respectively.

Step-by-step solution

Given Information 

The data in the Table are the result of a random survey of $39$national flags (with replacement between picks) from various countries.

$\begin{array}{|cc|}\hline \mathit{X}& \text{Freq.}\\ 1& 1\\ 2& 7\\ 3& 18\\ 4& 7\\ 5& 6\\ \hline\end{array}$

Explanation

We know that the mean number of colors on national flags was $3.26$, lower and upper limits of the confidence interval were $2.93$and $3.59$, respectively and

$1-\alpha =0.95\Rightarrow \frac{\alpha }{2}=0.025$

So, the graph for the problem is