You are working at a bank and doing resource planning. you think that there should be six tellers working in the bank. tellers take 15 minutes per customer with a standard deviation of 5 minutes. on average one customer arrives every three minutes according to an exponential distribution. a. on average how many customers are waiting in line? b. on average how long would a customer spend in the bank?

Lq = 1.680

time taken by customer 20.03 min

Step-by-step explanation:

Given data:

m = 6

a = 3 min

p = 15 minutes

CVa = 1

Number of customer waiting in line =

Lq = 1.679158

Lq = 1.680

FROM QUENNING FORMULA WE GET Tq =  5.039

so, time taken by customer = 5.039 + 15 = 20.03 min

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12