The maximum total production of a resource over a 10year per

The maximum total production of a resource over a 10-year period is found to be 57.6 percentage of the ultimate production of the resource. What fraction of the ultimate production is contained in the 20-year period of maximum total production? (Do NOT interpolate values in the probability table. Just choose the closest value.)

Solution

The probability lies symmetrical around mean.

Hence over 10 year period can be taken as 5 years to the left of mean and 5 years to the right of mean

X the random variable representing the production per year is Normal.

P(|x-mu|/sigma <5) = Area between -5 and +5 of the mean =57.6% = 0.576

From normal distribution we find z value corresponding to this.

|z|<0.8

So z corresponding to |x-mu|/sigma <10 will be

|z|<1.6

P(|z|<1.6) = 2(0.4452) = 0.8904

So approximately 89% will be covered in 20 years.