Question

Carbon monoxide? (CO) emissions for a certain kind of car vary with mean 3.977 ?g/mi and standard deviation 0.7 ?g/mi. A company has 60 of these cars in its fleet. Let y overbar represent the mean CO level for the? company's fleet. ?

a) What's the approximate model for the distribution of y overbar?? Explain.

?b) Estimate the probability that y overbar is between 4.1 and 4.3 ?g/mi. ?

c) There is only a 10?% chance that the? fleet's mean CO level is greater than what? value?

Answer 1

Solution:

Given that,

mean = = 3.977

standard deviation = = 0.7

n = 60

So,

a )   = 3.977

   =  ( /n) = (0.7 / 60 ) = 0.0904

b ) p ( 4.1 <   < 4.3 )

= p ( 4.1 - 3.977 / 0.0904) < ( -  / ) < ( 4.3 - 3.977 / 0.0904)

= p ( 0.102 / 0.0904 < z < 0.323 / 0.0904 )

= p ( 1.13 < z < 3.57 )

= p (z < 3.57 ) - p ( z < 1.13 )

Using z table

= 0.9998 - 0.8708

= 0.1290

Probability = 0.1290

c ) Using standard normal table,

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

P(Z < 1.28 ) = 0.90

z = 1.28

Using z-score formula,

= z * +

= 1.28 * 0.7 + 3.977

= 4.873

Value = 4.873