(See Steps) The serum cholesterol levels in men aged 18~24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7 . Units are in


Question: The serum cholesterol levels in men aged 18~24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7 . Units are in mg/100mL, and the data is based on the National Health Survey.

  1. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is greater than 260, a value considered "moderately high."
  2. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is between 170 and 200.
  3. If nine men aged 18-24 are randomly selected, find the probability that their serum cholesterol level is between 170 and 200.
  4. The Providence Health Maintenance Organization wants to establish a criterion for recommending dietary changes if cholesterol levels are in the top 3%. What is the cutoff for men aged 18-24?

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