The amount of a certain natural resin used in our factory in one month is a norm

Question

The amount of a certain natural resin used in our factory in one month is a normally distributed random variable with a mean value of 35.0 tons and of standard deviation of ± 4.2 tons.

What is the probability that this month our requirements for this resin will be greater than 30.0 tons, but less than 34.0 tons? Use at least four decimal places.

Continuing,

How much would you want to have on hand at the beginning of the month, if you want the probability to be 95% that we will have enough to meet our needs for that month? Give your answer to two (or more) decimal places. ( = 35.0 tons/month, and = 4.2 tons per month)

(There is no carry-over of this substance from one month to the next)

Explanation / Answer

given mean = 35

standard deviation = 4.2

p(x>30 <x<34) =

z= 30 -35 / 4.2 = 1.190

z = 34-35 / 4.2 = 0.238

p(x>30 <x<34) = 0.8830-0.5910 =0.2920 = 29.2%

, if you want the probability to be 95%

with same mean and standard deviation thn 0.95 *0.29= 0.2755

1-0.2755= 0.7245 = 72.45

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