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) normal distribution
B) Poisson distribution
C) uniform distribution
D) hypergeometric distribution

Question

Quizplus · Accepted Answer

The normal distribution can be used as an approximation to the binomial distribution when the sample size is large and the probability of success is neither very close to 0 nor 1. Here, with a large sample size of 100,000 and a probability of success of 0.8, the normal distribution is appropriate for approximating the probability of at least 90,000 alarms functioning properly.

The Probability That a Particular Brand of Smoke Alarm Will