Part2) Side Effects for Migraine Medicine (4 points)

In clinical trials and extended studies of a medication whose purpose is to reduce the pain associated with migraine headaches, 3% of the patients in the study experienced weight gain as a side effect. Suppose a random sample of 500 users of this medication is obtained.

Show your work or calculator functions to answer the following questions.

A.Explain why you can use normal approximation to the binomial distribution to approximate the probabilities below.

B.Approximate, up to 4 decimal digits, the probability that 15 or fewer users will experience weight gain as a side effect.

C.Approximate, up to 4 decimal digits, the probability that 24 or more users experience weight gain as a side effect.

D.Approximate, up to 4 decimal digits, the probability that between 12 and 20 patients, inclusive will experience weight gain as a side effect.