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

We need to find the probabilities of two events: 
1. P(x < 3)
2. P(x > 7)

Using the standard normal distribution formula, we can standardize x to z:

z = (x - μ) / σ 
where μ is the mean and σ is the standard deviation

For event 1: 
z = (3 - 2) / 5 = 0.2 
Using a standard normal distribution table, the probability of z less than 0.2 is 0.5793

For event 2: 
z = (7 - 2) / 5 = 1 
Using a standard normal distribution table, the probability of z greater than 1 is 0.1587

Therefore, the probabilities are not equal and the statement is false.

If X Is a Normal Random Variable with Mean of 2