The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. what is the probability density function for the time it takes to ring up a customer?

Step-by-step explanation:

The probability density function with exponential random variable T(t>0) with mean is given by :-

Given : The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes.

i.e.

Then , the probability density function for the time it takes to ring up a customer is :

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: