Question

Suppose X is a binomial random variable, where n=70, p= 0.8

Given that the distribution of X is symmetric, any observation that lies more than two standard deviations from the mean would be considered unusual. Therefore, usual observations would fall outside of the range:

a) [ 50.643, 54.982 ]

b) [ 49.306, 62.696 ]

c) [ 45.265, 66.432 ]

d) [ 52.653, 59.347 ]

Answer 1

Here, μ = n*p = 56, σ = sqrt(np(1-p)) = 3.348

mean +/- 2 *sd

=56 +/- 2 * 3.348

= (49.306,62.696)