Question

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decided to evaluate the satisfaction surveys of its next 62 customers. The dealer will be fined if the number of customers who report favorably is between 45 and 50. The dealership will be dissolved if fewer than 45 customers report. it is known that 84 % of the dealers customers report favorably on satisfaction surveys. ( use z table)

a) what is the probability that the dealer will be fined? round intermediate answers to 2 decimal places and round final answer to 4 decimal places.

b) what is the probability that the dealership will be dissolved? round intermediate answers to 2 decimal places and round final answer to 4 decimal places.

Answer 1

it is a binomial probability distribution,   because there is fixed number of trials,      
only two outcomes are there, success and failure      
trails are independent of each other      
and probability is given by      

P(X=x) = C(n,x)*px*(1-p)(n-x)

where  
Sample size , n =    62
Probability of an event of interest, p =   0.84

a)

probability that the dealer will be fined =P(45<X<50) = 0.1677

b)

P( the dealership will be dissolved ) = P(X<45) = P(X≤44) =0.0070