If X is a normal random variable with mean 6 and standard deviation 3.0, then find the value x such that P(Z

Question

If X is a normal random variable with mean 6 and standard deviation 3.0, then find the value x such that P(Z < x) is equal to .86, as shown below.(Note: the diagram is not necessarily to scale.) 
A)9.24 
B)7.32 
C)6.66 
D)6.00

Quizplus · Accepted Answer

Since X is a normal random variable with mean 6 and standard deviation 3.0, we can standardize it to a standard normal distribution using the formula Z = (X - µ) / σ. Substituting the values given, we get Z = (X - 6) / 3.0. We need to find x such that P(Z < x) = 0.86.

Using a standard normal distribution table, we can find that the Z-score corresponding to a probability of 0.86 is 1.08.

Therefore, we can write the equation (X - 6) / 3.0 = 1.08 and solve for X:

X = 6 + 3.0(1.08) = 9.24

So the answer is A: 9.24.

If X Is a Normal Random Variable with Mean 6