Given a normal distribution with $\mu=100$ and $\sigma=10$, complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that $X>85$ ? The probability that $X>85$ is $\square$. (Round to four decimal places as needed.)

Step 1 ：We are given a normal distribution with mean \(\mu = 100\) and standard deviation \(\sigma = 10\). We are asked to find the probability that a random variable X from this distribution is greater than 85.

Step 2 ：To find this, we first need to standardize the value 85 to a z-score. The z-score is the number of standard deviations a value is away from the mean. The formula for the z-score is \((X - \mu) / \sigma\).

Step 3 ：Substituting the given values into the formula, we get \(z = (85 - 100) / 10 = -1.5\).

Step 4 ：We then look up the corresponding probability in the z-table. However, the z-table gives us the probability that X is less than a certain value. So, we need to subtract the probability from 1 to get the probability that X is greater than 85.

Step 5 ：From the z-table, the probability corresponding to z = -1.5 is approximately 0.9332. Therefore, the probability that X > 85 is \(1 - 0.9332 = 0.0668\).

Step 6 ：However, since we are looking for the probability that X is greater than 85, we need to subtract this value from 1. So, the final probability is \(1 - 0.0668 = 0.9332\).

Step 7 ：Final Answer: The probability that \(X>85\) is \(\boxed{0.9332}\).