Question

Dawson's Repair Service orders parts from an electronic company, which advertises its parts to be no more than 4% defective. What is the probability that Bill Dawson finds 5 or more parts out of a sample of 100 to be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Answer 1

Here, μ = 4, σ = 1.9596 and x = 5. We need to compute P(X >= 5). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (5 - 4)/1.9596 = 0.51

Therefore,
P(X >= 5) = P(z <= (5 - 4)/1.9596)
= P(z >= 0.51)
= 1 - 0.695 = 0.3050

using continuity correction

Here, μ = 4, σ = 1.9596 and x = 5.5. We need to compute P(X >= 5.5). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (5.5 - 4)/1.9596 = 0.77

Therefore,
P(X >= 5.5) = P(z <= (5.5 - 4)/1.9596)
= P(z >= 0.77)
= 1 - 0.7794 = 0.2206