---
title: "Normal: bulb life between 750 and 825 h"
subject: "Probability and Statistics"
chapter: 3
key: "semester_5/probability_and_statistics:bulb-life-normal-750-825-900"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/bulb-life-normal-750-825-900
site: BCT Engineering
---

# Normal: bulb life between 750 and 825 h

Probability and Statistics · Chapter 3: Continuous Probability Distributions

- Asked in: 2074 Chaitra, 5 marks
- Video: [Normal Distribution - Example Problem 2 | Probability Distribution | Engineering Mathematics](https://www.youtube.com/watch?v=thmpqNzHy98) — Mathematics Tutor
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/bulb-life-normal-750-825-900
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-3

## Question

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

## 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.

## Answer

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**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. z for 750 hours is:
   A. -50
   B. +1.00
   C. -1.00
   D. -0.5
   Answer: C. (750 - 800)/50. (Key point: Standardise)

2. P(750 < X < 825) is:
   A. Phi(0.50) + Phi(-1.00)
   B. Phi(0.50) = 0.6915
   C. Phi(0.50) - Phi(-1.00) = 0.5328
   D. Phi(1.00) - Phi(0.5)
   Answer: C. Upper cumulative minus lower. (Key point: Between)

3. P(X > 900) is:
   A. 1 - Phi(2.00) = 0.0228
   B. Phi(2.00) = 0.9772
   C. 0.5 - 0.0228
   D. Phi(-2.00)=0.9772
   Answer: A. z = 2 and upper tail. (Key point: More than 900)

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