If random variable X follows the Normal distribution. X~Normal(10,10). Which amo

Question

If random variable X follows the Normal distribution. X~Normal(10,10). Which among the following statements are correct? Answer a. P(X<=10)=0.5 b. P(X=10)=0 c. P(X>8)=1-P(X<=7) d. P(3.3<X<=6)=P(X<=6)-P(X<=3.3) e. P(7.2<X<=4.2)=P(X<=4.2)-P(X<=7.2)

If random variable X follows the Normal distribution. X~Normal(10,10). Which among the following statements are correct? P(X<=10)=0.5 P(X=10)=0 P(X>8)=1-P(X<=7) a. P(X<=10)=0.5 b. P(X=10)=0 c. P(X>8)=1-P(X<=7) d. P(3.3<X<=6)=P(X<=6)-P(X<=3.3) e. P(7.2<X<=4.2)=P(X<=4.2)-P(X<=7.2)

Explanation / Answer

Correct statements are:

a) P(X<=10)=0.5

Area to the left of mean is equal to 0.5 in all case.

b) P(X=10)=0

In this case, the equation shows a point and a point always has area of 0

d) P(3.3<X<=6)=P(X<=6)-P(X<=3.3)

P(a<x<b) = P(x<a)-(P(x<b)

Equality sign doesn’t matter in above equation

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