The total cholesterol in US men ages $35-44$ is normally distributed with a mean of 209 and a standard deviation of 37.8 . Find the probability that a randomly selected man in this age group has a cholesterol below 220 (adapted from National Center for Health Statistics).
Use z-score and standard normal distribution table.
not enough information
0.291
0.3859
0.6141

Step 1 ：The problem is asking for the probability that a randomly selected man in this age group has a cholesterol below 220. This is a problem of normal distribution and we can solve it using the z-score formula. The z-score is a measure of how many standard deviations an element is from the mean. In this case, we need to calculate the z-score for a cholesterol level of 220, then look up this z-score in the standard normal distribution table to find the probability.

Step 2 ：Given that the mean cholesterol level is 209 and the standard deviation is 37.8, we can calculate the z-score for a cholesterol level of 220 using the formula \(z = \frac{x - \mu}{\sigma}\), where \(x\) is the value we are interested in (220), \(\mu\) is the mean (209), and \(\sigma\) is the standard deviation (37.8).

Step 3 ：Substituting the given values into the formula, we get \(z = \frac{220 - 209}{37.8} = 0.291\).

Step 4 ：We then look up this z-score in the standard normal distribution table to find the probability. The cumulative distribution function (cdf) gives the probability that a random variable is less than or equal to a certain value. In this case, it gives the probability that a randomly selected man in this age group has a cholesterol level below 220.

Step 5 ：The probability corresponding to the z-score of 0.291 is approximately 0.614.

Step 6 ：Final Answer: The probability that a randomly selected man in this age group has a cholesterol below 220 is approximately \(\boxed{0.614}\).