Question

75% of passengers travelling by metro train wear mask regularly when they travel . A random sample of 500 passengers are selected then find the probability that solution?

Answer 1

Find the probability that fewer than 400 of those in the sample regularly wear the mask.

$z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$

$p=0.75, p_0=400/500=0.8$

$z=\frac{0.75-0.8}{\sqrt{\frac{0.8\cdot0.2}{500}}}=-2.80$

$P(x<400)=P(z<-2.8)=0.00256$