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Question

Decide whether the following statements are true or false. Explain your answer. a. If X has a normal distribution with $\mu = 8,$ then $P(X \geq 8.21)=P(X \leq 7.79).$ b. If X has a normal distribution, then the probability is about 0.87 that its value will be within 1.5 standard deviations of the mean.

Solution

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1 of 3PART A:

Note that all normal distributions are symmetrical about their mean values. Furthermore, the points $X=8.21$ and $X=7.79$ are both equidistant from the mean $\mu=8$. Finally, the inequality signs also point in opposite directions. Therefore, we can conclude that $P\left(X\geq8.21\right)=P\left(X\leq7.79\right)$ is a true statement.

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