Question

Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.405 g/mi and standard deviation 0.7 g/mi. A company has 60 of these cars in its fleet. Let y represent the mean CO level for the​ company's fleet.

​a) What's the approximate model for the distribution of y ? mean and SD?

​b) Estimate the probability that y overbary is between 2.5 and 2.7 ​g/mi.

​c) There is only a 5% chance that the​ fleet's mean CO level is greater than what​ value?

Answer 1

Let -y represent the mean CO level for the company's fleet.

ans a)

mean of y-bar = mean of y = 2.405g/mi
std of y-bar or standard error(s.e)  = 0.7/sqrt(60) = 0.0904

ans b) at y bar = 2.5

z_2.5 =( 2.5 - 2.405 ) /0.0904 = 1.051

at y bar = 2.7

z_2.7 =( 2.7 - 2.405 ) /0.0904 =3.26

P ( 1.051 < z < 3.26 ) = normalcdf (1.051, 3.26 ,0,1) = 0.1463

the probability that y overbary is between 2.5 and 2.7 ​g/mi is  0.1463

ans c ) we know that invnorm(0.95,0,1) =1.645

z _0.05 =( y -  2.405) / 0.0904

1.645 * 0.0904 =   y -  2.405

0.14871+2.405 =y

y= 2.554

There is only a 5% chance that the​ fleet's mean CO level is greater than 2.554g/mi