Question

Suppose a company that makes fitness watches samples 15 watches. They know the probability one of their watches fails, within 1 year of purchase, is 0.12. The chance one watch fails is independent of other watches. What type of distribution will best model the number of watches out of the 15 sampled that fail within 1 year

Answer 1

Binomial probability distribution.

Explanation:

For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.