In studies for a medication 8 percent of patients gained wei

In studies for a medication, 8 percent of patients gained weight as a side effect. Suppose 736 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

A) Exactly 62 patients will gain weight as a side effect.

B) 62 or fewer patients will gain weight as a side effect

C) 35 or more patients will gain weight as a side effect

D) between 62 and 81 will gain weight as a side effect.

Please show step by step how you got the answers.

Solution

In studies for a medication, 8 percent of patients gained weight as a side effect. Suppose 736 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

Expectation = np = 58.88

Variance = np(1 - p) = 54.1696

Standard deviation = 7.36

P(x=62) = P(61.5<x<62.5)   ( with correction)

Z value for 61.5=(61.5-58.8)/7.36 =0.37

Z value for 62.5=(62.5-58.8)/7.36 =0.50

P(61.5<x<62.5) = p( 0.37<z<0.50) = P( z <0.50)