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Normal: bulb life between 750 and 825 h

Short answer

Z=(X-800)/50. (a) z1=-1, z2=0.5, P=Φ(0.5)−Φ(-1)=0.5328. (b) z=2, P=1−Φ(2)=0.0228.

The life of an electric light bulbs follows Normal distribution with mean 800 hours and a standard deviation of 50 hours. Find the probability that a bulb burns a) Between 750 and 825 hours b) More than 900 hours

X ~ N(μ = 800 h, σ = 50 h). Use Z = (X − 800)/50.

a) P(750 < X < 825)

z₁ = (750 − 800)/50 = −1.00, z₂ = (825 − 800)/50 = 0.50

P = Φ(0.50) − Φ(−1.00) = 0.6915 − 0.1587 = 0.5328

b) P(X > 900)

z = (900 − 800)/50 = 2.00

P = 1 − Φ(2.00) = 1 − 0.9772 = 0.0228

Answer: (a) 0.5328, (b) 0.0228

✓ Answer checked by Claude Sonnet 5.5

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