Question

The number of students using the School Bus per day is found in the distribution below.

X	15	25	10	12
P(X)	0.3	0.4	0.2	0.1

Find the mean , variance, and the standard deviation for this probability distribution.

Answer 1

Solution,

x	p(x)	x * p(x)	x2 * p(x)
15	0.3	4.5	67.5
25	0.4	10	250
10	0.2	2	20
12	0.1	1.2	14.4
Total	1.00	17.7	351.9

mean = = x * p(x) = 17.7

variance = 2  = x2 * p(x) - ( )2

variance = 2  = 351.9 - ( 17.7)2

variance = 2  = 351.9 - 313.29

variance = 2  = 38.61

standard deviation = =   2  = 38.61 = 6.21