Question

Light vehicles sold in a country must emit an average of no more than 0.06 grams per mile (g/mi) of nitrogen oxides (NOX) after 50,000 or fewer miles of driving. NOX emissions after 50,000 or fewer miles of driving for one car model vary Normally with mean 0.05 g/mi and standard deviation 0.01 g/mi.

(a) What is the probability that a single car of this model emits more than 0.06 g/mi of NOX? (Round your answer to four decimal places.)

(b) A company has 25 cars of this model in its fleet. What is the probability that the average NOX level x of these cars is above 0.06 g/mi? (Round your answer to four decimal places.)

You may need to use the appropriate Appendix Table to answer this question.

Answer 1

Solution :

Given that ,

mean = = 0.05

standard deviation = = 0.01

a) P(x > 0.06) = 1 - p( x< 0.06)

=1- p P[(x - ) / < (0.06 - 0.05) / 0.01]

=1- P(z < 1.00 )

Using z table,

= 1 - 0.8413

= 0.1587

b) n = 25

= = 0.05

= / n = 0.01 / 25 = 0.002

P( > 0.06) = 1 - P( < 0.06)

= 1 - P[( - ) / < (0.06 - 0.05) /0.002 ]

= 1 - P(z < 5)

Using z table,    

= 1 - 1

= 0