Question

Gas Mileage. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 MPG and a standard deviation of 3.5 MPG.

a) What is the probability that a randomly selected Cobalt gets more than 34 MPG?

b) Suppose that 10 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

c) Suppose 20 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

	A.	a) 0.284 b) 0.284 c) 0.284
	B.	a) 0.284 b) 0.035 c) 0.005
	C.	a) 2.84% b) 0.35% c) 0.05%
	D.	a) 28.4% b) 3.5% c) 0.5%

Answer 1

Solution :

Given that ,

mean = = 32

standard deviation = =3.5

P(x >34 ) = 1 - P(x < 34)

= 1 - P[(x - ) / < (34 - 32) /3.5 ]

= 1 - P(z <0.57 )

Using z table,

= 1 -0.7157

=0.284

(B)n = 10

= 32

= / n = 3.5 / 10 = 1.1068

P( >34 ) = 1 - P( 34< )

= 1 - P[( - ) / < (34 - 32) /1.1068 ]

= 1 - P(z <1.81 )

Using z table,    

= 1 - 0.9649

= 0.035

(C)n = 20

= 32

= / n = 3.5 / 20 = 0.7826

P( >34 ) = 1 - P( 34< )

= 1 - P[( - ) / < (34 - 32) / 0.7826 ]

= 1 - P(z <2.56 )

Using z table,    

= 1 - 0.9948

= 0.005