Question

Tickets to a concert are sold according to a poisson distribution with mean 30 per day.What are the probability that

i) less than 20 tickets are sold in one day

ii)all 180 tickets are sold in 5 day working week

Answer 1

Poisson distribution with $\lambda=30$ per day.

$p(x)=\frac{e^{-\lambda} \lambda^x}{x!}, x=0,1,2,...$

i. P(x<20)

$P(x<20)=\sum_{x=0}^{19}\frac{e^{-30} 30^x}{x!}$

The table below gives the values for x = 0-19

From the table, $\sum_{x=0}^{19}=0.02187$

Thus, $P(x<20)=0.02187$

=POISSON.DIST(19,30,TRUE) excel function can be used to obtain the solution.

ii. P(x=180) in 5 days

$\lambda=30\times5=150$

$p(180)=\frac{e^{-150} 150^{180}}{180!}$

$=0.00178$