Answer:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
The probability that an independent restaurant will fail in the first year is 32%.
This means that
72 independent restaurants
This means that
Mean:
Standard deviation:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.