Statistics Problem

Question

Based on observed males using public restroom, 85% of adult males wash their hands in public. In a survey of 523 males, 518 reported they wash their hands in public restrooms. Assuming the 85% rate is correct, find the probability that among 523 males, 518 or more wash their hands in public restrooms. What do you conclude with this result?

Answer 1

85% wash their hands in public

sample of 523 has 518 wash their hand in public

what is the probability of that happening?

85% = .85

.85 x 523 = about 445

calculate the z score

z= (518- 445)/s

then find the area under the curve between z=0 and the value above (but you need to know s=standard deviation)

or you could use a binomial distribution, since there are just 2 possibilities, wash or not wash

mean = np = 523(.85) = 445

variance = npq = 523(.85).15 = 445(.15) = about 67

standard deviation =sqr(npq) = sqr67) = about 8.166

(518-445)/8 = 73/8.166= 8.94=z

chances of being that far from the mean are nearly zero

same with probability of x>518

you might conclude that those males responding to your survey were exaggerating how often they wash

or you have an unreliable outlier, possible error in recording