Question

Find the missing value required to create a probability distribution, then find the standard deviation for the given probability distribution. Round to the nearest hundredth.

x / P(x)
////////
0 / 0.2
1 / 
2 / 0.13
3 / 0.03
4 / 0.05

Answer 1

Solution :

P(X)=0.2+0.13+0.03+0.05=0.41

total =0.41

sum of probabilities are equal to 1 than

P(1)=1-0.41=0.59

Mean = = X * P(X)

= 0 *0.2 + 1 * 0.59 + 2 *0.13 + 3 *0.03 + 4 *0.05

= ( 0+ 0.59 +0.26+0.09+0.2 )

Mean = = 1.14

Standard deviation =

=X 2 * P(X) - 2

=  [ 02 * 0.2 + 12 * 0.59 + 22 *0.13 + 32 *0.03 + 42 *0.05 ]-1.142

= [(0 + 0.59 + 0.52 + 0.27+0.8) )]-1.2996

=2.18-1.2996

=0.8804

Standard deviation = =0.94