Question

Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.3 g/mi and standard deviation 0.7 g/mi. A company has 80 of these cars in its fleet. Let y(overbar) represent the mean CO level for the​ company's fleet.

​a) Estimate the probability that y(overbar) is between 2.4 and 2.6 g/mi.

​b) There is only a 55​% chance that the​ fleet's mean CO level is greater than what​ value?

Show your work on TI-84

Answer 1

Solution:

Given that , Y follows a distribution with

= 2.3

= 0.7

A sample of size n = 80  is taken from this population.

Let   be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 2.3

SD =     = 0.7/80 =  0.07826237921

a)
To find P(2.4 < < 2.6) , Press 2nd and then press VARS. Then go to normalcdf

P(2.4 < < 2.6)

= normalcdf(2.4 , 2.6 , 2.3 , 0.07826237921)

= 0.1006050574

= 0.1006

b)

Find value of such that P(X > ) = 0.55

Use invNorm(

Required value

= 1 - invNorm(0.55 , 2.3 , 0.07826237921)

= 2.3098