Question

According to a study 50% of all males between the ages 18 and 24 live at home. suppose that a survey is administered and 127 of 226 respondents indicated that they live at home. a) use the normal approximation to the binomial to approximate the probability that at least 127 respondents live at home b) do the results for a) contradict the study?

Answer 1

a)

here mean of distribution=μ=np=		113.00
and standard deviation σ=sqrt(np(1-p))=		7.52
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability that at least 127 respondents live at home:

probability =P(X>126.5)=P(Z>(126.5-113)/7.517)=P(Z>1.8)=1-P(Z<1.8)=1-0.9641=0.0359

b)

since probability of above event is less than 0.05 which is unusual therefore it  contradict the study