## Related questions with answers

A binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. In a recent year, alcohol-impaired driving was the cause of 31% of motor vehicle fatalities. You randomly select 30 motor vehicle fatalities and determine whether alcohol-impaired driving was the cause.

Solution

VerifiedGiven:

$\begin{align*} n&=\text{Sample size}=30 \\ p&=\text{Probability of success}=31\%=0.31 \end{align*}$

Requirements for a normal approximation for the binomial distribution: $np\geq 5$ and $nq\geq 5$.

$\begin{align*} np&=30(0.31)=9.3\color{#4257b2}\geq 5 \\ nq&=n(1-p)=30(1-0.31)=20.7\color{#4257b2}\geq 5 \end{align*}$

Thus the requirements are satisfied.

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