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Probability word problem – please show me how to solve?
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 47.9 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 39 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated.
ANSWER: The probability of the sample greater than 48.5 = 32%.
Why???
NORMAL DISTRIBUTION, STANDARDIZED VARIABLE z, PROBABILITY “LOOK-UP”
STANDARDIZED VARIABLE: z = (x – µ)/(σ/√(n))
= (48.5 – 47.9)/(8/√(39)) =0.47
SAMPLE MEAN: x = 48.5
POPULATION MEAN: µ = 47.9
POPULATION STANDARD DEVIATION: σ = 8
SAMPLE SIZE: n = 39
SIGNIFICANT DIGITS = 2
The Table for Standard Normal Distribution is organized as a cummulative ‘area’ from the LEFT corresponding to the STANDARDIZED VARIABLE z. For STANDARDIZED VARIABLE GREATER THAN z = 0.47 the corresponding area = 0.32.
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