Question 18 Grades on a molecular biology exam are normally distributed with a mean of 346 and a standard deviation of 48 . Find the probability that a randomly selected student scores greater than 391. Round your answer to the thousandths place.

Step 1 ：The problem is asking for the probability that a randomly selected student scores greater than 391 on a molecular biology exam. The grades on this exam are normally distributed with a mean of 346 and a standard deviation of 48.

Step 2 ：In a normal distribution, the probability of a score being greater than a certain value is found by calculating the z-score of that value and then finding the area under the curve to the right of that z-score.

Step 3 ：The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. So, the z-score for the value 391 is calculated as \(\frac{391 - 346}{48} = 0.9375\).

Step 4 ：Once we have the z-score, we can use a z-table or a function like scipy's norm.sf (survival function, which is 1 - cdf) to find the probability. The probability corresponding to the z-score of 0.9375 is 0.17425071188054242.

Step 5 ：Final Answer: The probability that a randomly selected student scores greater than 391 is \(\boxed{0.174}\).