Question

Consider the following data: x 4 5 6 7 8 P(X=x) 0.2 0.2 0.1 0.2 0.3

Step 2 of 5: Find the variance. Round your answer to one decimal place.

Step 3 of 5: Find the standard deviation. Round your answer to one decimal place.

Step 4 of 5: Find the value of P(X<7). Round your answer to one decimal place

Step 5 of 5:Find the value of P(X≥7). Round your answer to one decimal place.

Answer 1

Solution :

Mean = = X * P(X)

= 4 *0.2 + 5 *0.2 + 6 * 0.1+ 7 * 0.2 + 8 * 0.3

= (0.8+1+0.6 +1.4 +2.4 )

= 6.2

Standard deviation =

=X 2 * P(X) - 2

=  [    42 *0.2 + 52 *0.2 + 62 * 0.1+ 72 * 0.2 + 82 * 0.3]-6.22

= [( 3.2+ 5+3.6 +9.8+19.2 ) )] -38.44

= 40.8-38.44

=2.36

Standard deviation = =1.5

variance =2

=X 2 * P(X) - 2

=  [    42 *0.2 + 52 *0.2 + 62 * 0.1+ 72 * 0.2 + 82 * 0.3]-6.22

=  [( 3.2+ 5+3.6 +9.8+19.2 ) )] -38.44

= 40.8-38.44

variance =2=2.4

(C)P(X<7)=P(X=4)+P(X=5)+P(X=6)

=0.2+0.2+0.1

probability =0.5

(D) P(X≥7)=P(X=7)+P(X=8)

=0.2+0.3

=0.5

probability=0.5