I'm stuck on the following problem:

The percentage of fat in the bodies of American men is an approximately normal random variable with mean equal to 15% and standard deviation equal to 2%.

a. If these values were used to describe the body fat of men in the United States Army and if 20% or more body fat is characterized 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 chec the percentage of body fat for a random sample of 10,000 men and if only 30 contained 20% (or higher) body fat, would you conclude that the army was successful in reducing the percentage of obese men below the percentage of the general population? Explain your reasoning.

I am very stuck. So far, I used the equation mean = np = (10,000)(.15) = 1500. Also, took the square root of npq to get standard deviation of approximately 35.71. However, I don't even know if this is right and I am very much confused by all the figures. Thanks in advance