Question

What is the probability that we will have exactly 4 non-negative observations out of 10 randomly-generated observations from N(0, 1)

Answer 1

0.21

Explanation:

Given a distribution :

N(0, 1) - - - > Normal distribution

Probability of obtaining a non - negative observation :

P(x ≥ 0) = 0.5 ( Z probability calculator)

Hence, p = 0.5 ; (1 - p) = 1 - 0.5 = 0.5

P(x = 4) :

Using the binomial probability function :

P(x = x) = nCx * p^x * (1 - p)^(n-x)

P(x = 4) = 10C4 * 0.5^4 * 0.5^10 - 4

P(x = 4) = 210 * 0.0625 * 0.015625

P(x = 4) = 0.205078125

P(x = 4) = 0.21