Question

In studies for a​ medication, 88 percent of patients gained weight as a side effect. Suppose 476 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​

(a) exactly 39 patients will gain weight as a side effect. (Round to four decimal places as​ needed)

​(b) no more than 39 patients will gain weight as a side effect. (Round to four decimal places as​ needed)

​(c) at least 48 patients will gain weight as a side effect. What does this result​ suggest? (Round to four decimal places as​ needed)

Answer 1

n=

476

p=

0.0800

here mean of distribution=μ=np=	38.08
and standard deviation σ=sqrt(np(1-p))=	5.919
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

a)

probability =P(38.5<X<39.5)=P((38.5-38.08)/5.919)<Z<(39.5-38.08)/5.919)=P(0.07<Z<0.24)=0.5948-0.5279=0.0669

b)

probability =P(X<39.5)=(Z<(39.5-38.08)/5.919)=P(Z<0.24)=0.5948

c)

probability =P(X>47.5)=P(Z>(47.5-38.08)/5.919)=P(Z>1.59)=1-P(Z<1.59)=1-0.9441=0.0559

(since above is not less than 0.05 , getting 48 patients gaining weight as a side effect is not an unusual event.)