Given a normally distributed random variable X with a µ=5 and σ=2, find P(X>8).Question 4Answera.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 convert the X value to a z-score. The z-score is a measure of how many standard deviations an element is from the mean.

The formula for finding the z-score is:

Z = (X - µ) / σ

where: X = value for which we want to find the probability (8 in this case) µ = mean of the distribution (5 in this case) σ = standard deviation of the distribution (2 in this case)

Substituting the given values into the formula, we get:

Z = (8 - 5) / 2 = 1.5

Now, we need to find the probability that Z is greater than 1.5 (P(Z>1.5)). We can find this probability from the standard normal distribution table or use a calculator with a normal distribution function.

However, the standard normal distribution table usually gives the probability that Z is less than a given value (P(Z<z)). So, to find P(Z>1.5), we need to subtract P(Z<1.5) from 1.

P(Z>1.5) = 1 - P(Z<1.5)

Looking up 1.5 in the Z-table or using a calculator, we find that P(Z<1.5) is approximately 0.9332.

So, P(Z>1.5) = 1 - 0.9332 = 0.0668

Therefore, the probability that X is greater than 8 (P(X>8)) is approximately 0.0668. So, the correct answer is (d) 0.0668.