If X is a normal random variable with mean of 2 and standard deviation of 5,then P(X 7).

Question

If X is a normal random variable with mean of 2 and standard deviation of 5,then P(X < 3)= P(X > 7).

Quizplus · Accepted Answer

Using the standard normal distribution, we can convert the values to z-scores: For P(X < 3): z = (3 - 2)/5 = 0.2 Using a standard normal distribution table or calculator, we find P(z < 0.2) = 0.579 For P(X > 7): z = (7 - 2)/5 = 1 Using a standard normal distribution table or calculator, we find P(z > 1) = 0.159 Since 0.579 is not equal to 0.159, we can see that P(X < 3) is not equal to P(X > 7), so the statement is false.

If X Is a Normal Random Variable with Mean of 2