Monthly utility bills are normally distributed with a mean of $120

Mathematics
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and a standard deviation of $16?
a) what is the probability that a randomly selected bill will be less than $80 per month? 


b) what is the probability that a bill will be greater than $140 per month? 

c) what is the probability that a bill will be between $100 & $140 per month? 

if someone could explain this to me, this chapter has me lost
Apr 22nd, 2015

a)  Z = 80-120 / 16 = -2.5 standard deviations from the mean

look up on Z chart to find probability:  P = .0062 or 0.062%

b) Z = 140-120 / 16 = 1.25 standard deviations from the mean

on Z chart, the probability = 0.8944, but that is the probability for LESS THAN $140

for GREATER THAN we need to subtract it from 1:  1 -0.8944 = 0.1056 or 10.56%

c) for between $100 and $140 we have to subtract the probability of each

P(Z at $140) = 0.8944

P(Z at $100) = 0.1056

The difference is 0.7888 or 78.88%

Apr 22nd, 2015

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Apr 22nd, 2015
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Apr 22nd, 2015
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