To Determine the Effectiveness of a Diet to Reduce the Amount

Essay

To determine the effectiveness of a diet to reduce the amount of serum cholesterol, 20 people were randomly selected to try the diet. After they had been on the diet a sufficient amount of time, their blood was tested to determine the level of serum cholesterol. The clinic running the experiment will approve and endorse the diet only if at least 16 of the 20 people lower their cholesterol significantly.
What is the random variable of interest?
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What is the probability the clinic will erroneously endorse the diet when, in fact, it is useless in treating high serum cholesterol?