Question

# In studies for a​ medication, 88 percent of patients gained weight as a side effect. Suppose...

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)

 n= 476 p= 0.08
 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

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.)