Question

# Consider the following data: x 44 55 66 77 88 P(X=x) 0.20. 0.10 0.30. 0.20. 0.20....

Consider the following data:

 x P(X=x) 44 55 66 77 88 0.20. 0.1 0.30. 0.20. 0.20.

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

Step 3 of 5: Find the standard deviation

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

Step 5 of 5:

Step 5 of 5: Find the value of P(X<6). Round your answer to one decimal place.

We need to find P(X>5) and P(X<6) so assuming x takes values as 4,5,6,7,8 and not 44,55,66,77,88

 x P(X=x) 4 5 6 7 8 0.20. 0.1 0.30. 0.20. 0.20.

1) E(X) = sum(p(x)*x)

= 0.20*4 + 0.10*5 + 0.30*6 + 0.20*7 + 0.20*8

= 6.1

2) Variance = E(X^2) - (E(X))^2

= (0.20*4^2 + 0.10*5^2 + 0.30*6^2 + 0.20*7^2 + 0.20*8^2) - (6.1)^2

= 1.89

3)

Standard deviation = sqrt(Variance)

= sqrt(1.89) = 1.37

4)

P(X > 5) = P(X = 6) + P(X =7) + P(X=8)

= 0.3 + 0.2 + 0.2

= 0.7

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

= 0.2 + 0.1

= 0.3

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