Question

A statistical consultant discovers that when a person makes a dinner reservation, there is a 0.0091 chance he or she will not show up. A restaurant, therefore, routinely books 30 reservations even though they only have 26 tables.
(a) What is the probability a person does show up for their reservation?



(b) What is the probability that more than 26 people show for their reservation?



(c) Based on the probability from part (b), should the restaurant adjust its practices? Why or why not?

Answer 1

a)

probability a person does show up for their reservation =1-0.0091 =0.9909

b)

here this is binomial with parameter n=30 and p=0.9909

  probability that more than 26 people show for their reservation:

P(X>=27)=1-P(X<=26)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.9998

(note:

if using ti-84 use command :1-binomcdf(30,0.9909,26)

if using excel use command :1-binomdist(26,30,0.9909,true)

c)

since probabiltiy of having 27 or more people is very high, restaurant should adjust its practices , otherwise they need to return customers who have made the reservation very often which will not be good for its reputation