Question

A meteorologist in denver recorded y = the number of days of rain during a 30-day period. does y have a binomial distribution? if so, are the values of both n and p given?

Answer 1

Solution: Yes, the random variable y will have a binomial distribution. Because there are two possible outcomes 1. number of days of rain and 2. number of days of no rain.

The parameters of binomial distribution are $n$ and $p$

The parameter n is given as the number of day's under consideration.

$\therefore n=30$

The parameter p is not given, but it can be estimated by number of days it rained divided by the total number of days under consideration.

$\therefore p=\frac{y}{n} =\frac{y}{30}$