Question

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?

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%