Question

1. Carbon monoxide (CO) emissions for a certain kind of vehicle vary according to a normal distribution with mean µ = 2.9 g/mi and standard deviation σ = 0.4 g/mi.
   1. What percent of vehicles are within one standard deviation of the mean?
   2. Above what level of emissions are the top 40% of vehicles?
   3. EPA standards require these types of vehicles to emit no more than 4.2 g/mi.  Would it be unusual for a randomly selected vehicle of this type to exceed the EPA standard?
   4. Would it be unusual for the mean emissions of a random sample of 16 vehicles to emit more than 3 g/mi? Give support for your answer.

Answer 1

Mean, = 2.9

Standard deviation, = 0.4

(a) 68.26% of the vehicles are within one standard deviation of the mean

(b) Corresponding to top 40%, the z value = 0.2533

Thus, the required emission = 2.9 + 0.2533*0.4 = 3.001 g/mi

(c) Probability that the emission is greater than or equal to 4.2 g/mi = P{Z ≥ (4.2 - 2.9)/0.4} = P(Z ≥ 3.25) = 0.0006

Yes, it would be unusual because this probability is very low (less than 0.05)

(d) For n = 16, standard error = 0.4/√16 = 0.1

Probability that the mean emission from a sample of 16 vehicles is more than 3 g/mi = P{Z > (3 - 2.9)/0.1}

= P(Z > 1) = 0.1587

So, it would not be unusual