The amount of floor glue needed by a carpet laying crew for a one-day shift is u

Question

The amount of floor glue needed by a carpet laying crew for a one-day shift is uniformly distributed between the values of 8 and 16 gallons.

Question:

Every night the contruction company who hires the carpet laying company needs to stock pile the amount of floor glue needed for the next day's shift. How many gallons of floor glue should they have in stock at the beginning of each day if they want to have enough glue on hand so that they only run out 5% of the time? Is this value the 5th or the 95th percentile?

Explanation / Answer

amount of floor glue needed by a carpet laying crew for a one-day shift is uniformly distributed between the values of 8 and 16 gallons

if X is uniformly distributed between (a,b),P(X<=x) = (x-a)/(b-a)

let X be the amount of floor glue needed by a carpet laying crew for a one-day shift

so X is iniformly distributed between 8 and 16 (according to given data)

we need to find amount of glue i.e X that they need to have in stock if they want to have enough glue on hand so that they only run out 5% of the time

let the value of glue that they need to have in stock if they want to have enough glue on hand so that they only run out 5% of the time be A

so P(X>A) = 5% or 0.05

P(X<A) = 1-0.05 = 0.95

so (A-8)/(16-8) = 0.95

A -8 = 0.95*8 = 7.6

A = 15.6

This value of X i.e 15.6 is greater than 95% of values than X can take

so 15.6 is   95th percentile

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