Question

18 watches are built each week.

Apiece, a watch has a .50 (50%) probability of working.

Each week is profitable if nine or less watches fail to pass the evaluation.

When there is a profitable week, I receive a 5 rubber ducks.

How many rubber ducks will I get in a year?

Answer 1

first we will find the probability of having a profitable week.

this can be done using binomial probability distribuytion, with probability of success(probability of a watch working ): p = 0.50

total number of watches: n= 18

the week will be profitable if 9 or less watches fail.

the probability week will be profitable is

in a year there is a total of 52 weeks

Hence the expected number of profitable weeks is 52*0.5927=30.8204

for every profitable week I receive 5 rubber ducks

hence you can expect a rubber ducks in a year