Body fat in men. The percentage of fat in the bodies of some men is an approximately normal random variable with mean equal to 20% and standard deviation equal to 4%.

a. If these values were used to describe the body fat of men in the army, and if a measure of 30% or more body fat characterizes the person as obese, what is the approximate probability that a random sample of 10,000 soldiers will contain fewer than 50 who would actually be characterized as obese?

b. If the army actually were to check the percentage of body fat for a random sample of 10,000 men, and if only 30 contained 30% (or higher) body fat, would you conclude that the army was successful in reducing the percentage of obese men below the percentage in the general population? Explain your reasoning.