Question

6. In a study of used car prices, a sample of dealerships in a large city showed a wide discrepancy in the final sales prices. For 50 cars of identical specifications, the following prices were recorded:

            Prices                                     Relative Frequency

$19200< $19400                                          .10

$19400< $19600                                          .20

$19600< $19800                                          .40

$19800< $20000                                          .30

a. Approximate the mean selling price of these 50 used cars. (6 pts)

b. Approximate the median selling price of a used car. (6 pts)

7. A study of loss payment per insurance claim by homeowners showed an average of $1810, with a standard deviation of $90.

a. If the distribution of loss payments is bell-shaped, then what percentage of payments is above $1990? (6 pts

b. What percentage of payments is below $1720? (6 pts)

Answer 1

6)

a) mean selling price = Σfx = 19680

b) median = 19700

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7)

a)

µ =    1810                  
σ =    90                  
                      
P ( X ≥   1990   ) = P( (X-µ)/σ ≥ (1990-1810) / 90)              
= P(Z ≥   2.00   ) = P( Z <   -2.000   ) =    0.0228   (answer)

b)

µ =    1810          
σ =    90          
              
P( X ≤    1720   ) = P( (X-µ)/σ ≤ (1720-1810) /90)      
=P(Z ≤   -1.00   ) =   0.1587   (answer)