Question

Consider the following data:

x	4	5	6	7	8
P(X=x)	0.2	0.2	0.1	0.2	0.3

Copy Data

Step 1 of 5:

Find the expected value E(X). Round your answer to one decimal place.

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≤8). Round your answer to one decimal place.

Step 5 of 5:

Find the value of P(X>4). Round your answer to one decimal place.

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
4	0.2	0.8	3.2
5	0.2	1	5
6	0.1	0.6	3.6
7	0.2	1.4	9.8
8	0.3	2.4	19.2
Sum	1	6.2	40.8

From given probability distribution,

1)

Mean = = X * P(X)

E(X) =   = 6.2

(2)

Variance = ²

= X ² * P(X) - ²

V(X) = 40.8 - 6.2²

= 2.36

(3)

standard deviation = 1.5

4)

P(X 8) = 1.0

(5)

P(X > 4) = 1 - P(X 4) = 1 - 0.2 = 0.8