Question

The following table presents the probability distribution of the number of vacations X taken last year...

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the standard deviation .

x 0 1 2 3 4

p(x) .07 .66 .16 .07 .04

Math   Statistics-And-Probability   
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Answer #1

Solution :

Mean = = X * P(X)

= 0 *0.07 + 1 * 0.66+ 2 *0.16 + 3 *0.07 + 4 *0.04

= ( 0+ 0.66 + 0.32 +0.21+0.16 )

= 1.35

Standard deviation =

=X 2 * P(X) - 2

=  [ 02   * 0.07 + 12 * 0.66+ 22 *0.16 + 32 *0.07 + 42 *0.04] -1.352

= [( 0+ 0.66+0.64 +0.63+0.64 ) )] -`1.8225

= 2.57 -1.8225

=0.7475

=0.8646

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