x is a normally distributed random variable with a mean of 6 and a variance of 4. The probability that x is greater than 8.75 is
A) 0.9154.
B) 0.0846.
C) 0.0775.
D) 0.9225.

Question

Quizplus · Accepted Answer

First, we need to calculate the standard deviation of x, which is the square root of the variance: sqrt(4) = 2. 
Next, we standardize the value we are interested in by subtracting the mean and dividing by the standard deviation: (8.75 - 6)/2 = 1.375. 
Using a standard normal distribution table or a calculator with a normal distribution function, we find that the probability of a standard normal variable being greater than 1.375 is approximately 0.0846. Therefore, the answer is B) 0.0846.

X Is a Normally Distributed Random Variable with a Mean