Question

If X is a normal random variable with mean 85 and standard deviation 10, compute P(X>90). Round to four decimal places.

A. 0.3085
B. 0.3849
C. 0.6915
D. 0.7699

Answer 1

To compute the probability P(X > 90), we need to find the area to the right of 90 on the normal distribution curve. Using the z-score formula, we can standardize the variable and find the corresponding probability using a standard normal distribution table.

Step-by-step explanation:

To compute the probability P(X > 90), we need to find the area to the right of 90 on the normal distribution curve. We can do this by standardizing the variable X using the z-score formula: z = (X - mean) / standard deviation. Plugging in the values, we have: z = (90 - 85) / 10 = 0.5. Using a standard normal distribution table, we can find the probability corresponding to this z-score. The answer is approximately 0.3085, which corresponds to option A.