Question 10, 7.2.23 HW Score: $71.11 \%, 10.67$ of 15 points Part 2 of 2 Points: 0 of 1 Save 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. \[ P(X>38) \] Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to $P(X>38)$ ? A. \[ P(X>38)=\square \] (Round to four decimal places as needed) example Get more help - Clear all Check answer

Step 1 ：Given that the random variable $X$ is normally distributed with mean $\mu=50$ and standard deviation $\sigma=7$, we are asked to compute the probability $P(X>38)$.

Step 2 ：First, we need to standardize the value 38 to a z-score. The z-score is the number of standard deviations a particular value is from the mean. It is calculated using the formula: \(z = \frac{x - \mu}{\sigma}\).

Step 3 ：Substituting the given values into the formula, we get: \(z = \frac{38 - 50}{7} = -1.7142857142857142\).

Step 4 ：Next, we look up this z-score in a standard normal distribution table to find the probability. However, since the table usually gives the probability that a value is less than a certain value, we need to subtract the result from 1 to get the probability that the value is greater than 38.

Step 5 ：Doing this, we find that the probability corresponding to the z-score is approximately 0.9567618672531671.

Step 6 ：Finally, we round this probability to four decimal places to get the final answer: $P(X>38) = \boxed{0.9568}$.