Question

In a survey, three out of four students said that courts show too much concern for criminals. Find the probability that of seventy randomly selected students

At least 56 feel that courts show too much concern

Answer 1

Probability that a student show too much concern for criminals

= 3/4 = 0.75

Let X be a Binomial random variable which denotes the number of students out of seventy students who show too much concern for animals

n = 70, p = 0.75

Thus , np = 52.5 and np(1-p) = 13.125

So X can be approximated to Normal distribution with

Mean = 52.5 and

standard deviation = √13.125 = 3.623

The required probability = P(X ≥ 56)

Using correction of continuity, P(X ≥ 56) = P(X > 55.5)

= P{Z > (55.5 - 52.5)/3.623}

= P(Z > 0.828)

= 0.2039