Question

Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 51%. She obtains a random sample of 84 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.

Answer 1

Answer: Mean = 42.84

Standrad deviation = 4.58

Explanation:

Given: The probability that an independent restaurant will fail in the first year : p = 51% = 0.51

Sample size: n= 84

Since restaurant as two possible outcomes either fail or succeed. So it is a binomial problem.

Mean = np = (84)(0.51) =42.84

Standard deviation =
`√(np(1-p))=√((84)(0.51)(1-0.51))`

`=√((84)(0.51)(0.49))\\\\=√(20.9916)\approx4.58`

Hence, Mean = 42.84

Standrad deviation = 4.58