The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. A batch of 100,000 such alarms was produced by independent production lines. Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?
A) Exponential distribution
B) Poisson distribution
C) Normal distribution
D) Uniform distribution

Question

Quizplus · Accepted Answer

We would use the normal distribution to figure out the probability of at least 90,000 smoke alarms functioning properly in case of a fire. This is because the sample size of 100,000 is sufficiently large and the probability of success (0.8) is not too close to 0 or 1. We can use the normal distribution to approximate the binomial distribution (which would be the exact distribution in this case) using the mean (80,000) and standard deviation (400) of the binomial distribution.

The Probability That a Particular Brand of Smoke Alarm Will