Problem

For the graph shown above, find the given probability. Use the Empirical Rule (68-95-99.7) and do not round any answers. a. $P(X<35)$ : b. $P(3567)$ :

Solution

Step 1 :Given that the mean (μ) is 50 and the standard deviation (σ) is 15, we can use the Empirical Rule to find the probabilities.

Step 2 :For a. $P(X<35)$, since 35 is one standard deviation below the mean, the probability is approximately 16% (100% - 68% / 2).

Step 3 :For b. $P(35

Step 4 :For c. $P(X>67)$, since 67 is one standard deviation above the mean, the probability is approximately 16% (100% - 68% / 2).

Step 5 :So, the final answers are: a. $P(X<35)$ : \(\boxed{16\%}\), b. $P(3567)$ : \(\boxed{16\%}\)

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Source: https://solvelyapp.com/problems/36088/

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