Question

Suppose Clay, a grocery store owner, is monitoring the rate at which customers enter his store. After watching customers enter for several weeks, he determines that the amount of time in between customer arrivals follows an exponential distribution with mean 25
What is the 70th percentile for the amount of time between customers entering Clay's store? Round your answer to the nearest two decimal places. 70th percentile

Answer 1

Answer:

70th percentile for the amount of time between customers entering is 30.10

Step-by-step explanation:

given data

mean =  25

to find out

What is the 70th percentile for the amount of time between customers entering Clay's store

solution

we know that here mean is

mean = $\frac{1}{\lambda}$   ..................1

so here 25 =  $\frac{1}{\lambda}$

and we consider time value corresponding to 70th percentile = x

so we can say

P(X < x) = 1 - $e^{- \lambda *x}$      

P(X < x) = 70 %

1 - $e^{\frac{-x}{25}}$  = 70 %

1 - $e^{\frac{-x}{25} }$  = 0.70

$e^{\frac{- x}{25} }$  = 0.30

take ln both side

$\frac{-x}{25}$ = ln 0.30

$\frac{x}{25}$  = 1.203973

x = 30.10

70th percentile for the amount of time between customers entering is 30.10