Polychtonnated biphenyl PCB is among a group of organic poll

Polychtonnated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulatir>g materials, and lubricants m electncal equipment Disposal ot items containing less than 50 parts per million (ppm) PCB is generally not regulated A certain Kind ot small capacitor contains PCB with a mean of 48 ppm and a standard deviation of 6 ppm The Environmental Protection £gcncy takes a random sample of 37 ot those small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 ppm of more Find the probability that the disposal of such capacitors will be regulated Cany your intermediate computations to at least four decimal places Round your answer to at teast three decimal places

Solution

Sample mean >= 49.5, it can be disposed.

Sample size =37

Population mean = 48 std dev = 6

z score for mean 49.5

is z >= (49.5-48)/6/rt 37 = 1.521

P(Z>1.521) = 0.5-0.4357

= 0.0643.