---
title: "Breakdown voltage: three ranges"
subject: "Probability and Statistics"
chapter: 3
key: "semester_5/probability_and_statistics:bv-39-42-40-43-lt44"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/bv-39-42-40-43-lt44
site: BCT Engineering
---

# Breakdown voltage: three ranges

Probability and Statistics · Chapter 3: Continuous Probability Distributions

- Asked in: 2071 Shrawan, 5 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/bv-39-42-40-43-lt44
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-3

## Question

The breakdown voltage X of a randomly chosen diode of a particular type is known to be normally distributed with mean 40 volts and variance 2.25 volts. What is the probability that the breakdown voltage will be:
i) Between 39 and 42 volts
ii) Between 40 and 43 volts
iii) Less than 44 volts

## Short answer

Standardize with sigma=1.5. The probabilities are (i) 0.6568, (ii) 0.4772, and (iii) 0.9962.

## Answer

X ~ N(μ = 40, σ² = 2.25), so σ = 1.5, and Z = (X − 40)/1.5.

#### i) P(39 < X < 42)
z₁ = (39 − 40)/1.5 = −0.67, z₂ = (42 − 40)/1.5 = 1.33

P = Φ(1.33) − Φ(−0.67) = 0.9082 − 0.2514 = **0.6568**

#### ii) P(40 < X < 43)
z₁ = 0, z₂ = (43 − 40)/1.5 = 2.00

P = Φ(2.00) − Φ(0) = 0.9772 − 0.5000 = **0.4772**

#### iii) P(X < 44)
z = (44 − 40)/1.5 = 2.67

P = Φ(2.67) = **0.9962**

**Answer: (i) 0.6568, (ii) 0.4772, (iii) 0.9962**

## Check yourself

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

1. P(40 < X < 43) is:
   A. Phi(2.00) - Phi(0) = 0.4772
   B. Phi(2.00) = 0.9772
   C. Phi(2.00) + 0.5
   D. 1 - 0.9772
   Answer: A. z for 40 is 0, with Phi(0) = 0.5. (Key point: Between 40 and 43)

2. z-values for 39 and 42 are:
   A. -1 and 2
   B. 0.67 and 1.33
   C. -0.67 and 2.00
   D. -0.67 and 1.33
   Answer: D. (39-40)/1.5 and (42-40)/1.5. (Key point: Between 39 and 42)

3. P(X < 44) is:
   A. 1 - 0.9962
   B. Phi(2.67) = 0.9962
   C. Phi(4)-Phi(0)
   D. 0.4962 exactly
   Answer: B. Lower-tail area is read directly. (Key point: Less than 44)

## Close variants set in other exams

- [Breakdown voltage: normal, variance 2.25](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Abv-39-42-lt44-gt43) — Probability and Statistics, chapter 3, asked 3×

## Related in Probability and Statistics

- [Breakdown voltage: normal probabilities (1.5 V)](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Abv-39-42-le43-ge39) — Probability and Statistics, chapter 3, asked 3×

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- [When terminal voltage is less or more than emf](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-less-or-more) — Electric Machines II, chapter 1