Question

The CO emissions produced by a family of 1.6L engines as measured on a standardized test is normally distributed with a mean of 124 ppm (ppm = parts per million) and a standard deviation of 12 ppm. We want to establish an upper limit in ppm on emissions for this engine that will be exceeded only 2% of the time. That upper limit would be approximately

Answer 1

Solution:-

Given that,

mean = = 124

standard deviation = =12

Using standard normal table,

P(Z > z) = 2%

= 1 - P(Z < z) = 0. 02

= P(Z < z) = 1 - 0.02

= P(Z < z ) = 0.98

= P(Z < 2.05) = 0.98  

z = 2.05 ( using z table )

Using z-score formula,

x = z * +

x = 2.05 * 12+124

x = 148.6

x=149