The amount of sulfur dioxide escaping from the ground in a certain volcanic regi

Question

The amount of sulfur dioxide escaping from the ground in a certain volcanic region in one day is normally distributed with a mean mu = 500 tons and a standard deviation sigma = 50 tons under ordinary conditions. However, if a volcanic eruption is imminent, there are much larger sulfur dioxide emissions. (a) Under ordinary conditions, what is the probability of there being a daily sulfur dioxide emission larger than 625 tons? (b) What is the 99th percentile of daily sulfur dioxide emissions under ordinary conditions? (c) If your instruments indicate that 700 tons of sulfur dioxide have escaped from the ground on a particular day, would you advise that an eruption is imminent? Why? How sure would you be?

Explanation / Answer

a).

z value for 625, z =(625-500)/50 = 2.5

P( x >625) =P( z >2.5)

= 0.0062

b).

z value for 99th percentile =2.326

x value for 99th percentile=mean+z*sd

=500+2.326*50

= 616.3

c).

z value for 700, z =(700-500)/50 = 4

P( x >700) =P( z >4)

=0.000032

Since the P( x>700)=0.000032 is unusual event (<0.05),we advise that an eruption is imminent.

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