Question

A certain statistical test is designed so that it fails 2% of the time. Suppose that 400 of these tests are randomly selected, and we wish to calculate the proportion of these tests that result in a failure. What is the probability that less than 1.5% of these tests end in failure?

Answer 1

Here, μ = 0.02, σ = 0.007 and x = 0.015. We need to compute P(X <= 0.015). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (0.015 - 0.02)/0.007 = -0.71

Therefore,
P(X <= 0.015) = P(z <= (0.015 - 0.02)/0.007)
= P(z <= -0.71)
= 0.2389