Question

7. Consider the following data:

x 6 7 8 9 10

P( X = x ) 0.3 0.1 0.2 0.1 0.3

Step 1 of 5: Find the expected value E(X) 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<9)P(X<9). Round your answer to one decimal place.

Step 5 of 5: Find the value of P(X≥9)P(X≥9). Round your answer to one decimal place.

Answer 1

7)

Solution :

Mean = = X * P(X)

= 6 * 0.3 + 7 * 0.1 + 8 * 0.2 + 9 * 0.1 + 10 * 0.3

E(X) = 8

variance =

= X ² * P(X)

=  6² * 0.3 + 7² * 0.1 + 8² * 0.2 + 9² * 0.1 + 10² * 0.3 - 8²

=  2.6

variance = 2.6

Standard deviation = = 2.6 = 1.6

P(X < 9) = 0.3 + 0.1 + 0.2 = 0.6

P(X 9) = 1 - P(X < 9) = 1 - 0.6 = 0.4