SOLUTION: Please help! I cannot figure this one out! I asked my teacher too and she gave me the wrong answers :/
A car manufacturer is concerned about poor customer satisfaction at one o
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Question 977868: Please help! I cannot figure this one out! I asked my teacher too and she gave me the wrong answers :/
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 69 customers. The dealer will be fined if the number of customers who report favorably is between 40 and 46. The dealership will be dissolved if fewer than 40 report favorably. It is known that 73% 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
b. What is the probability that the dealership will be dissolved? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Probability
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
This is a problem using the Sampling Distribution of the Proportion
The mean of the sample is .73
standard deviation of the sample is square root(PQ/n) where P=0.73, Q=0.27 and n =69
standard deviation of the sample is square root(0.73*0.27/69) = 0.053446438
***********************************************************************
mean(p) = 0.73 and std dev(p) = 0.05
40/69 = 0.579710145 approx 0.58
46/69 = 0.666666667 approx 0.67
***********************************************************************
a) Probability(P) ( 40 < X < 46 ) = P ( X < 46) - P ( X < 40 )
z-value for 46 is (0.67 - 0.73) / 0.05 = -1.2 and
P ( X < 46 ) = 0.1151
z-value for 40 is (0.58 - 0.73) / 0.05 = -3 and
P ( X < 40 ) = 0.0013
therefore
Probability(P) ( 40 < X < 46 ) = 0.1151 - 0.0013 = 0.1138
b) P ( X < 40 ) = 0.0013
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