If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:
A)0.125.
B)0.975.
C)0.625.
D)0.500.

Question

Quizplus · Accepted Answer

When we have a normal distribution, we can standardize the variable using the formula Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation. This transformation converts our original variable into a standard normal variable, which has a mean of 0 and a standard deviation of 1.

In this case, we want to find P(X ≤ 75), which is the same as P(Z ≤ 0) if we standardize X. Since our standard normal variable has a mean of 0, the probability of being less than or equal to the mean is 0.5. Therefore, P(Z ≤ 0) = 0.5, and P(X ≤ 75) = 0.5.

So the correct answer is D: 0.500.

If the Random Variable X Is Normally Distributed with a Mean