Question

The probability distribution for the random variable X is given below. X 0 P(x) 0.05 0.17 0.26 2 3 4 0.24 0.28 What is the standard deviation to the nearest hundredth) for the random variable? O A 1.17 OB. 12 O C. 1.3 OD. 124 O E. None of the above Click to select your answer Type here to search o i E

Answer 1

Answer:

Data given:

The probability distribution for the random variable X is given below as -

0	0.05
1	0.17
2	0.26
3	0.24
4	0.28

Standard deviation for the random variable,  $\sigma$ = ?

As we know, the formula for computing the standard deviation for the random variable X is given as -

Standard deviation, σ = Σ(x?P(X) – ΣXP(x))?

Using the above information, we can find the standard deviation for the random variable X as -

		$X^{2}$		$X^{2}.P(X)$
0	0.05	0	0	0
1	0.17	1	0.17	0.17
2	0.26	4	0.52	1.04
3	0.24	9	0.72	2.16
4	0.28	16	1.12	4.48
			$\sum X.P(X) = 2.53$	$\sum X^{2}.P(X) =7.85$

Standard deviation, σ = Σ(x?P(X) – ΣXP(x))?

  $= \sqrt {7.85- (2.53)^{2}}$

$= \sqrt {7.85- 6.4009}$

$= \sqrt {1.4491}$

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Thus, the standard deviation for the random variable X is approximately 1.20 .

Hence, the correct option is (B) .