Assume that the random variable $X$ is normally distributed, with mean $\mu=53$ and standard deviation $\sigma=10$. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. \[ P(X \leq 42) \] Which of the following shaded regions corresponds to $P(X \leq 42)$ ? A. B. c. $P(X \leq 42)=$ (Round to four decimal places as needed.)

Step 1 ：Assume that the random variable $X$ is normally distributed, with mean $\mu=53$ and standard deviation $\sigma=10$. We are asked to compute the probability $P(X \leq 42)$, which corresponds to the area under the normal curve to the left of 42.

Step 2 ：To find this probability, we need to standardize the value 42 to a z-score, which gives us the number of standard deviations 42 is away from the mean. The formula for the z-score is $z = \frac{x - \mu}{\sigma}$, where $x$ is the value we're interested in (42 in this case), $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step 3 ：Substituting the given values into the z-score formula, we get $z = \frac{42 - 53}{10} = -1.1$.

Step 4 ：After finding the z-score, we can use a z-table or a statistical function to find the probability that $X$ is less than or equal to 42. The probability is approximately 0.13566606094638267.

Step 5 ：Rounding to four decimal places, the probability that the random variable $X$ is less than or equal to 42 is approximately 0.1357. This means that there is a 13.57% chance that a randomly selected value from this distribution will be less than or equal to 42.

Step 6 ：Final Answer: The probability that $X$ is less than or equal to 42 is approximately \(\boxed{0.1357}\).