A car manufacturer is concerned about poor customer satisfaction at one of its d

Question

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 50 customers. The dealer will be fined if the number of customers who report favorably is between 32 and 34. The dealership will be dissolved if fewer than 32 report favorably. It is known that 78% of the dealer’s customers report favorably on satisfaction surveys. Use Table 1. a. What is the probability that the dealer will be fined? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability =

(I have tried .0570 and .0590 and they are both incorrect)

Explanation / Answer

Here n=50 and p=0.78

As np>10, we wll use approximation to normal

Now mean=np=39 and sd=sqrt(np(1-p))=2.93

So P(32<x<34)=P(32-39/2.93<z<34-39/2.93)=P(-2.39<z<-1.71)=0.0352

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