Question

In a population of 1,000,000 people, 1000 have particular disease. You are at a gathering of 200 random
people. Use a normal approximation to find the probability that at least one person at the gathering
has the disease (use continuity correction)

Answer 1

Population proportion that people have the disease is =p = 1000/1000000 = 0.001

Our sample size is = n= 200

By normal approximation we have

Mean = n×p = 200×0.001 = 0.2

Variance=np(1-p) = 0.2 ×(1-0.001) =0.1998

Sd = 0.447

So we can take X is the number of people having the disease and X ~ Normal (0.2,0.1998)

Now we need to find,

By applying the continuity correlation for normal approximation we now calculate

=

=

=

=

= 1 - 0.7486 [From Z table]

= 0.2514