Question

If 5% of the parts produced from a manufacturing process are defective, what is the probability that there are 30 or more defectives in a random sample of 500 items?

a) 0.2475

b) 0.6515

c) 0.1515

d) 0.8485

e) 0.3485

Answer 1

Here, μ = 25, σ = 4.8734 and x = 30. We need to compute P(X >= 30). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (30 - 25)/4.8734 = 1.03

Therefore,
P(X >= 30) = P(z <= (30 - 25)/4.8734)
= P(z >= 1.03)
= 1 - 0.8485 = 0.1515

Option C