# Thread: Simple problem, normal distribution

1. ## Simple problem, normal distribution

How would you answer this? Police have proved 45% of people the give speeding tickets to are aged between 18-25. If they pull over 8 people what is the probability that 6 are aged 18-25?

Thank you!!

2. ## Re: Simple problem, normal distribution

Originally Posted by ictodd
How would you answer this? Police have proved 45% of people the give speeding tickets to are aged between 18-25. If they pull over 8 people what is the probability that 6 are aged 18-25?

Thank you!!
This is not a normal distribution problem but a binomial distribution problem. Number r of people in a sample of N in the age bracket is:

$\displaystyle b(r;N,0.45)=\frac{N!}{(N-r)!r!}(0.45)^r(0.55)^{N-r}$

The sample size would have to be much larger than 8 for the use of the normal approximation to be valid, though the binomial calc gives a probability of 6.88% and the normal in this case 7.03%.

If you want to try the normal approximation calculation start by calculating the mean and standard deviation $\displaystyle \mu,\ \sigma$ of the number of people in the given age group pulled over. Then you need to compute the probability using the normal distribution $\displaystyle N(\mu, \sigma^2)$ of between $\displaystyle 5.5$ and $\displaystyle 6.5$.

CB