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Fill in the missing information. Enter percentage answers to the nearest tenth.

Jim Tree wants to analyze another shipment of trees based on height. He knows the height of the trees is normally distributed so he can use the standard normal distribution. He measures the height of 500 randomly selected trees in his shipment. Next, he calculates the mean and standard deviation of their heights. The mean is 60 inches, and the standard deviation is 12 inches. Now, Jim uses the normal distribution table above to calculate the number of trees in each segment of the distribution.

\begin{tabular}{|c|c|c|}
\hline
Standard Deviation & Percentage from table & Number of trees out of 500 \\
\hline
-1 to 0 (48 to 60 inches) & [tex]$34.1\%$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
0 to +1 (60 to 72 inches) & [tex]$34.1\%$[/tex] & 171 \\
\hline
+1 to +2 (72 to 84 inches) & [tex]$13.6\%$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Let's fill in the missing information step by step.

First, let's find the boundary height for the segment from 0 to +1 standard deviation:
- The mean height is 60 inches.
- The standard deviation is 12 inches.
- From 0 to +1 standard deviation is from 60 inches to (mean + 1 standard deviation) = 60 + 12 = 72 inches.

Next, let's determine the percentage from 0 to +1 standard deviation:
- Given that there are 500 trees in total and 171 of them fall into the 0 to +1 standard deviation segment.
- The percentage of trees in this segment is (171 / 500) 100 = 34.2%.

Finally, let's determine the number of trees from +1 to +2 standard deviation:
- The standard deviation from +1 to +2 corresponds to 13.6% of the distribution.
- The number of trees in this segment is (13.6 / 100) 500 = 68 trees.

Therefore, the completed table is:

\begin{tabular}{|c|c|c|}
\hline Standard Deviation & Percentage from table & Number of trees out of 500 \\
\hline -1 to 0 (48 to 60 inches) & 34.1\% & 171 \\
\hline 0 to +1 (60 to 72 inches) & 34.2\% & 171 \\
\hline +1 to +2 (72 to 84 inches) & 13.6\% & 68 \\
\hline
\end{tabular}
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