Consider a normal population with a mean of 10 and a variance of 4.Find P(X ≥ 10).
A)1.00
B)0.00
C)0.50
D)-0.50

Question

Quizplus · Accepted Answer

To find P(X ≥ 10), we need to find the area to the right of 10 on a standard normal distribution curve. However, we don't have a standard normal distribution in this case, we have a normal population with mean 10 and variance 4.

We can standardize the distribution by using the z-score formula:

z = (x - μ) / σ

where x is the value we're interested in (in this case, 10), μ is the mean of the population (10), and σ is the standard deviation of the population (sqrt(4) = 2).

Plugging in the values, we get:

z = (10 - 10) / 2 = 0

This tells us that 10 is exactly at the mean of the population, so the area to the right of 10 (i.e. P(X ≥ 10)) is exactly 0.5.

Therefore, the answer is C.

Consider a Normal Population with a Mean of 10 and a Variance