Question

Washing Hands

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

Answer 1

here expected number of people among 523 who wash their hands in a public restroom

=np=523*0.85=444.55

and std deviaton =sqrt(np(1-p))=8.166

therefore from normal approximation:

probability that among 523 randomly selected adult males, 518 or more wash their hands in a public restroom=P(X>=518)=P(Z>(517.5-444.55)/8.166)=P(Z>8.93) =~0.0000

as probability of among 523 randomly selected adult males, 518 or more wash their hands in a public restroom is almost negligible, ; therefore we conclude that proportion of males who  wash their hands in a public restroom must be higher than 85%.