Given a normally distributed random variable X with a µ=5 and σ=2, find P(X>8).Question 2Answera.0.0001b.0.9270c.0.1862d.0.0668

To find the probability that a normally distributed random variable X is greater than 8 (P(X>8)), we first need to standardize this value using the Z-score formula:

Z = (X - µ) / σ

where: X is the value we are interested in (in this case, 8), µ is the mean of the distribution (in this case, 5), and σ is the standard deviation of the distribution (in this case, 2).

Substituting these values into the formula, we get:

Z = (8 - 5) / 2 = 1.5

Next, we look up this Z-score in a standard normal distribution table, or use a calculator or software that can compute it. The value we get from the table is the probability that the variable is LESS than our value. But we want the probability that it is MORE than our value. So we subtract the value from 1.

The value for Z=1.5 is approximately 0.9332. So, P(X>8) = 1 - 0.9332 = 0.0668.

So, the answer is d. 0.0668.