Question

In studies for medication, 11 percent of patients gained weight as a side effect. Suppose 402...

In studies for medication, 11 percent of patients gained weight as a side effect. Suppose 402 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

a) exactly 45 patients gain weight as a side effect

b) no more than 45 patients will gain weight as a side effect

c) at least 53 patients will gain weight as a side effect. What does this result suggest?

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Answer #1

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Answer:

n= 402 p= 0.1100
here mean of distribution=μ=np= 44.22
and standard deviation σ=sqrt(np(1-p))= 6.2734
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

a)

probability = P(44.5<X<45.5) = P(-0.0446<Z<0.2040)= 0.0630

b)

probability = P(X<45.5) = P(Z<0.2040)= 0.5808

c)

probability = P(X>52.5) = P(Z>1.319858)= 0.0934

as the probability of this event is significant low, therefore this may indciate that percentage is lower than 11%

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