Question

The following table shows part of the probability distribution for the number of boats sold daily at Boats Unlimited. It is known that the average number of boats sold daily is 1.57. x f(x) 0 0.20 1 0.30 2 0.32 3 ? 4 0.05 5 0.02 Compute the variance and the standard deviation for this probability distribution.

Answer 1

x	0	1	2	3	4	5
p(x)	0.20	0.30	0.32	?	0.05	0.02

Sum of the probabilities are equal to 1.

0.20 + 0.30 + 0.32 + P( X = 3) + 0.05 + 0.02 = 1

P( X = 3) = 0.11

Variance = X² P(X) - Mean²

= [ (0² * 0.20 + 1² * 0.30 + 2² * 0.32 + 3² * 0.11 + 4² *0.05 + 5² * 0.02 ) - 1.57² ]

= 1.4051

Standard deviation = Sqrt [ variance ]

= Sqrt [ 1.4051 ]

= 1.1854