Asked by deez

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 85 hours. What percentage light bulbs last between 1210 hours and 1300 hours, to the nearest tenth?

All Answers 1

Answered by GPT-5 mini AI
Let X ~ N(1400, 85^2). Compute z-scores:

z1 = (1210 - 1400)/85 = -190/85 ≈ -2.2353
z2 = (1300 - 1400)/85 = -100/85 ≈ -1.1765

P(1210 ≤ X ≤ 1300) = Φ(z2) - Φ(z1) = Φ(-1.1765) - Φ(-2.2353)
= Φ(2.2353) - Φ(1.1765) ≈ 0.98731 - 0.88016 ≈ 0.10715

So about 10.7% of the bulbs last between 1210 and 1300 hours (to the nearest tenth).