One of the cars sold by Walt\'s car dealership is a very popular subcompact car

Question

One of the cars sold by Walt's car dealership is a very popular subcompact car called Rhino. The final sales price of the basic model of this car varies from customer to customer depending on the negotiating skills and persistence of the customer. Assume that these sales prices of this car are normally distributed with a mean of $19800 and a standard deviation of $300. a. Dolores paid $19445 for her Rhino. What percentage of Walt's customers paid less than Dolores for a Rhino? b. Cuthbert paid $20300 for a Rhino. What percentage of Walt's customers paid more than Cuthbert a Rhino? c. What price for a Rhino corresponds to the lower 5% of Walt's customers?

Explanation / Answer

a) please check mean price =19800 (as it seems blurry)

std deviation =300

P(X<19445)=P(Z<(19445-19800)/300) =P(Z<-1.1833)=0.1183

b)P(X>20300)=1-P(X<20300) =1-P(Z<1.6667)=1-0.9522=0.0478

c) for lower 5% , z=-1.6449

hence corresponding value =19800-1.6449*300=19306.53

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