Assume the random variable $X$ is normally distributed with mean $\mu=50$ and standard deviation $\sigma=7$. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. \[ P(X>34) \] Click the icon to view a table of areas under the normal curve. Which of the following normal carves corresponds to $P(X>34)$ ? A. B. c. \[ P(X>34)= \] (Round to four decimal places as needed.)

Step 1 ：Given a normally distributed random variable $X$ with mean $\mu=50$ and standard deviation $\sigma=7$, we are asked to find the probability that $X$ is greater than 34, i.e., $P(X>34)$.

Step 2 ：First, we need to standardize the value 34 to a z-score. The z-score is the number of standard deviations a particular value is from the mean. The formula for the z-score is $z = \frac{X - \mu}{\sigma}$.

Step 3 ：Substituting the given values into the formula, we get $z = \frac{34 - 50}{7} = -2.2857142857142856$.

Step 4 ：Next, we use a z-table or a standard normal distribution table to find the probability corresponding to the z-score. The z-table gives us the probability that a standard normal random variable is less than a given value. But we want the probability that $X$ is greater than 34, so we need to subtract the value from the z-table from 1.

Step 5 ：Doing this, we get $P(X>34) = 1 - P(Z < -2.2857142857142856) = 0.9888645105203836$.

Step 6 ：Rounding to four decimal places, we get $P(X>34) = 0.9889$.

Step 7 ：So, the probability that the random variable $X$ is greater than 34 is approximately \(\boxed{0.9889}\).