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Probability

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Question : 85 of 127

Marks: +1, -0

What is the standard deviation of

x ?

X :	1	2	4	5	6
P :	$0.15$	$0.25$	$0.20$	$0.30$	$0.10$

$1.49$
$1.69$
$1.56$
$1.72$

Solution:

Concept:

Standard deviation measures the spread of a probability distribution; it is the square root of the variance.

Explanation:

First, compute the mean

\mu = \sum x \cdot P(x)

:

1(0.15) + 2(0.25) + 4(0.20) + 5(0.30) + 6(0.10) = 0.15 + 0.50 + 0.80 + 1.50 + 0.60 = 3.55

.

Next, compute

\sum x^2 P(x)

:

1^2(0.15) + 2^2(0.25) + 4^2(0.20) + 5^2(0.30) + 6^2(0.10) = 0.15 + 1.00 + 3.20 + 7.50 + 3.60 = 15.45

.

Variance

\sigma^2 = \sum x^2 P(x) - \mu^2 = 15.45 - (3.55)^2 = 15.45 - 12.6025 = 2.8475

.

Standard deviation

\sigma = \sqrt{2.8475} \approx 1.687

, which rounds to

1.69

.

Answer:

1.69

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