The variable $x$ takes on integer values between $1$ and $7$ inclusive as shown above. What is the probability

$\begin{array}{cc}
x & \text{frequency}\\
1 & 3\\
2 & 1\\
3 & 3\\
4 & 1\\
5 & 3\\
6 & 1\\
7 & 3\\
\end{array}$

The variable $x$ takes on integer values between $1$ and $7$ inclusive as shown above. What is the probability that the absolute value of the difference between the mean of the distribution which is $4$ and a randomly chosen value of $x$ will be greater than $\dfrac32?$

A) $\dfrac8{15}$

B) $\dfrac47$

C) $\dfrac45$

D) $\dfrac67$

E) $\dfrac87$

Answer: A

Source: GMAT Prep

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