Question

5. In Salinas, 68% of adults have health insurance. If 400 adults were randomly selected. a) Find the probability that at least 230 of them have health insurance. (Use binomial approximation) b) Find the probability that exactly 230 of them have health insurance. (Use binomial approximation)

Answer 1

(here if possible ask ur instructor if 230 figure is ok; as it is far away from mean and therefore almost no calculation is required in both a and b)

a)

here expected number of people having heath insurance =np=400*0.68=272

and std deviaiton=sqrt(np(1-p))=9.330

hence from normal approximation of binomial distribution:

for normal distribution z score =(X-μ)/σ
here mean=       μ=	272
std deviation   =σ=	9.330

probability of having at least 230 with health insurance"

probability =P(X>=230)=

P(X>229.5)

=

P(Z>-4.56)=

1-P(Z<-4.56)=

1-0=

1.0000

b)

probability of having exactly 230 of them have heath insurance:

probability =

P(229.5<X<230.5)

=

P(-4.56<Z<-4.45)=

0-0=

0.0000