- 2070 Chaitra · 4 marks
Normal: machinery assembly time
Short answer
a) z=(11.5−12.9)/2=−0.70, P(Z≥−0.70)=0.7580. b) z-scores −0.95 and 0.95, probability = 2×0.3289=0.6578.
The time required to assemble a piece of machinery is a random variable having approximately a normal distribution with mean 12.9 minutes and standard deviation of 2 minutes. What are the probabilities that the assembly of a piece of machinery of this kind will take (a) at least 11.5 minutes (b) between 11.0 to 14.8 minutes?
Assembly time X ~ N(μ = 12.9, σ = 2) minutes.
a) At least 11.5 minutes
z = (11.5 − 12.9)/2 = -0.70
P(X ≥ 11.5) = P(Z ≥ −0.70) = 0.5 + P(0 < Z < 0.70) = 0.5 + 0.2580 = 0.7580
b) Between 11.0 and 14.8 minutes
- z₁ = (11.0 − 12.9)/2 = -0.95
- z₂ = (14.8 − 12.9)/2 = 0.95
P(11.0 < X < 14.8) = P(−0.95 < Z < 0.95) = 2 × 0.3289 = 0.6578
Answer: a) 0.7580 b) 0.6578
✓ Answer checked by Claude Sonnet 5.5
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