Compute the Mean and Standard Deviation of a Binomial Random Variable
-According to insurance records, a car with a certain protection system will be recovered 94% of the time. If 300 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered after being stolen
A) mean: 282; standard deviation: 4.11339276
B) mean: 282; standard deviation: 16.92
C) mean: -618: standard deviation: 4.11339276
D) mean: -618: standard deviation: 16.92

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $n \times p$, where $n$ is the number of trials and $p$ is the probability of success. Here, $n = 300$ and $p = 0.94$, so the mean is $300 \times 0.94 = 282$. The standard deviation is given by $\sqrt{n \times p \times (1-p)}$, which calculates to $\sqrt{300 \times 0.94 \times (1-0.94)} = 4.11339276$.