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 / 0.09
1 / 
2 / 0.17
3 / 0.18
4 / 0

Answer 1

Solution :

solution

P(X)=0.09+0.17+0.18+0=0.44

total=0.44

sum of probabilities are equal to 1

P(1)=1-0.44=0.56

Mean = = X * P(X)

= 0 *0.09 + 1 *0.56 + 2 *0.17 + 3 * 0.18 + 4 * 0

= ( 0+ 0.56 +0.34+0.54+0 )

= 1.44

Standard deviation =

=X 2 * P(X) - 2

=  [ 02   0.09 + 12 *0.56 + 22 *0.17 + 32* 0.18 + 42 * 0]-1.442

= [( 0+ 0.56+0.68+1.62 + 0) )] -2.0736

= 2.86-2.0736

=0.7864

Standard deviation = =0.89