Question

In a study on honesty, Canadian respondents were asked to imagine they had just made a purchase at a store and that the cashier gave them $10 extra in change by mistake. Do they hand the money back? The study reported that 74% of adults said they would return the money, while only 35% of teens said they would return the money. Assume that the percentages quoted in the study are accurate for the population of adults and teens in Canada.

Find the probability that in a random sample of 100 Canadian teens:

(a) 30 say they would return the money.

(b) At least 20, but at most 35, say they would return the money.

Round your final answers to 4 decimal places.

Please answer all parts of the question.

Answer 1

here for binomial distribution parameter n=100 and p=0.35

here mean of distribution=μ=np=		35.0000
and standard deviation σ=sqrt(np(1-p))=		4.7697
for normal distribution z score =(X-μ)/σx
since np and n(1-p) both are greater than 5, we can use normal approximation of binomial distribution
therefore from normal approximation of binomial distribution and continuity correction:

a)

P( 30 say they would return the money):

probability =P(29.5<X<30.5)=P((29.5-35)/4.77)<Z<(30.5-35)/4.77)=P(-1.15<Z<-0.94)=0.1736-0.1251=0.0485

b)

P( At least 20, but at most 35 ):

probability =P(19.5<X<35.5)=P((19.5-35)/4.77)<Z<(35.5-35)/4.77)=P(-3.25<Z<0.1)=0.5398-0.0006=0.5392