Light vehicles sold in US must emit an average of no more th

Light vehicles sold in US must emit an average of no more than 0.07 grams per mile of nitrogen oxides (NOx). For Toyota sold in US, NOx emission has a Normal distribution with mean 0.065 g/mi and standard deviation of 0.01 g/mi, i.e. N (µ= 0.065, = 0.01)

What is the probability that one randomly selected Toyota vehicle to have NOx emission higher than 0.07 g/mi?

What is the chance that the average NOx emission of the 10 Toyota vehicles selected to be higher than 0.07 g/mi?

Solution

Light vehicles sold in US must emit an average of no more than 0.07 grams per mile of nitrogen oxides (NOx). For Toyota sold in US, NOx emission has a Normal distribution with mean 0.065 g/mi and standard deviation of 0.01 g/mi, i.e. N (µ= 0.065, = 0.01)

What is the probability that one randomly selected Toyota vehicle to have NOx emission higher than 0.07 g/mi?

Z value of 0.07, z=( 0.07-0.065)/0.01 =0.5

P( x >0.07) = p( z >0.5)

= 0.3085

What is the chance that the average NOx emission of the 10 Toyota vehicles selected to be higher than 0.07 g/mi?

Standard error = sd/sqrt(n)= 0.01/sqrt(10) =0.0032

Z value of 0.07, z=( 0.07-0.065)/0.0032 =1.56

P( mean x >0.07) = p( z >1.56)

= 0.0594