5.) Diesel Dave has modiÖed his massive truck to combat global cooling, and to roll coal on his neighbor Environmentalist Ed. With each blast of diesel exhaust fumes, Diesel Dave releases sulfur dioxide in a giant black cloud. Every morning as Diesel Dave is leaving home he rolls coal into Environmentalist Edís yard. Not surprisingly, Environmentalist Ed is diligently collecting data on the air quality in his yard. Suppose Diesel Dave releases sulfur dioxide in a normally distributed manner with a mean of 2800 ppm and a standard deviation of 120 ppm. What is the probability that on a random morning he will release sulfur dioxide greater than 3000 ppm?

You want to know the probability of a release greater than 3000 ppm, given that releases are normally distributed with a mean of 2800 ppm and a standard deviation of 120 ppm.

Normal CDF

The probability can be found using a spreadsheet or statistical calculator to evaluate the normal CDF function.

P(X > 3000) ≈ 0.04779 ≈ 4.8%

The probability of interest is about 4.8%.

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Additional comment

The attachment shows the probability to as many significant figures as you may want. We have rounded to 2 significant figures, because the problem numbers have that precision.