Question

In a survey at a local college, 18% of students reported that they do not own a mobile device with internet capabilities. if 20 students are selected at random, find the probability that at most 5 students don't own a mobile device with internet capabilities.

Answer 1

0.64

Explanation:

The probability that randomly selected student doesn't own a mobile device with internet capabilities is
`p=0.18` and the probability that randomly selected student owns a mobile device with internet capabilities is
`q=1-p=1-0.18=0.82.`

If 20 students are selected at random, the probability that at most 5 students (0 students, 1 student, 2 students, 3 students, 4 students or 5 students) don't own a mobile device with internet capabilities is

`Pr=C_(20)^0p^0q^(20)+C_(20)^1p^1q^(19)+C_(20)^2p^2q^(18)+C_(20)^3p^3q^(17)+C_(20)^4p^4q^(16)+C_(20)^5p^5q^(15)=q^(20)+20pq^(19)+190p^2q^(18)+1,140p^3q^(17)+4,875p^4q^(16)+15,504p^5q^(15)\approx 0.6405021423\approx 0.64.`