Question

5 Assume that the cost of a certain model of new car is normally distributed with a mean of $25,000 and a standard deviation of $2000.

a Find the probability that a car chosen at random from this model will cost $29,500 or more b Find the probability it will cost $18,000 or less

b	Find the probability it will cost $18,000 or less

Answer 1

Solution :

Given that,

mean = = $ 25,000

standard deviation = =$ 2000.

A ) P ( x > 29,500 )

= 1 - P (x < 29,500 )

= 1 - P ( x -  / ) < ( 29,500 - 25,000 / 2000.)

= 1 - P ( z < 4500 / 2000.)

= 1 - P ( z < 2.25 )

Using z table

= 1 - 0.9878

= 0.0122

Probability = 0.0122

B) P ( x <18000 )

P ( x -  / ) < ( 18000 -  25,000 / 2000.)

P ( z < - 7000 / 2000.)

P ( z < - 3.5 )

Using z table

0.0002

Probability = 0.0002