The selling price of a new car is normally distributed with an average of $24920 and a variance of $11492100.00

Question

A) What proportion of new cars will sell for less than $17730? 

probability =

B) Assuming a normal distribution, within what selling prices will the middle 93% fall? 

lower= upper=

Answer 1

If variance = 11492100, SD = 3390.

z = (17730 - 24920) / 3390 = -7190 / 3390 = -2.12.

Probability of (z < -2.12) = 0.017.

Middle 93% means excluding the top 3.5% and bottom 3.5%, so the area is between cumulative probabilities of 0.035 and 0.965. This is the area between z = -1.812 and z = +1.812.

So the boundaries of the middle 93% are 24920 +/- (1.812 * 3390) = 24920 +/- 6143 = 18777 to 31063.