Question

The time required to assemble a piece of machinery is a random variable with mean 12.9 min and variance 4 min. what are the probabilities that the assembly of a piece of machinery of this kind will take.

a) at least 11min

b) anywhere from 12 to 14 min

Answer 1

a)

Here, μ = 12.9, σ = 2 and x = 11. We need to compute P(X >= 11). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (11 - 12.9)/2 = -0.95

Therefore,
P(X >= 11) = P(z <= (11 - 12.9)/2)
= P(z >= -0.95)
= 1 - 0.1711 = 0.8289

b)
Here, μ = 12.9, σ = 2, x1 = 12 and x2 = 14. We need to compute P(12<= X <= 14). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (12 - 12.9)/2 = -0.45
z2 = (14 - 12.9)/2 = 0.55

Therefore, we get
P(12 <= X <= 14) = P((14 - 12.9)/2) <= z <= (14 - 12.9)/2)
= P(-0.45 <= z <= 0.55) = P(z <= 0.55) - P(z <= -0.45)
= 0.7088 - 0.3264
= 0.3824