Question

The amount of gas (in parts per million, ppm) measured by a device is normally distributed. The probability of gas level below 2 ppm is 20% and the probability of gas level above 8 ppm is 10%.

1. What should be the standard deviation (?) such that the probability of gas level between 3 ppm and 7 ppm is 95%?

Answer 1

a.

According to the Emperical Rule of normal distribution approximately 95% of the data falls within two standard deviations of the mean

If be the mean of the distribution and be the standard deviation of the distribution

Then by emperical rule 95% of the data falls between and

Here,

So,

Answer: The standard deviation () should be 1 ppm