Let X is the random variable denoting dule'tn of car wash.

car wash in 4 stages.

$\therefore k = 4$

each stage is exponentially dist. with mean time = 9 minutes.

i.e. $KQ = \frac{1}{9}$

$\therefore$ The probability that the car wash will take 30 mins/less is given by

p ( x ≤ 30) = f (30)

$= 1 - \sum^k-1_i=0 \frac{e^-kqx (kqx)^i}{i !} 1 x \gt 0$

$= 1 - /sum^3_i\lt0 \frac{e^\frac{-1}{09^30} [ \frac{1}{09} \times 30]^i} {i !}$

= 1 - [ 0.0238 + 0.1192 + 0.1985 + 0.2203]

= 1 - 0.5738

= 0.4262

$E(x) = \frac{1}{0} = \frac{1}{1/60} = 60 mins$

$u(x) = \frac{1}{kq^2} = \frac{1}{4 (1/60)^2} = 900 mins^2$

model value (made)

$= \frac{k-1}{kq}$

$= \frac{4.1}{1/9}$

= 27 mins.