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Fundamental Principle of Counting

Let X denote ...

Question

Let X denote the number of scores which exceed 4 in 1 toss of a symmetrical die. Consider the following statements :
1. The arithmetic mean of X is 6.
2. The standard deviation of X is 2.
Which of the above statements is/are correct ?

1 only

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2 only

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Both 1 and 2

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Neither 1 nor 2

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Solution

The correct option is C Neither 1 nor 2
The only possible favorable outcomes are $5$ and $6$ . Hence, the arithmetic mean of $X$ is 5.5.
The standard deviation of $X = \frac{1}{2} ((6 - 5.5)^{2} + (5 - 55)^{2}) = 0.25$

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