Question

A hotel claims that 85% of its customers are very satisfied with its service. Complete parts a through d below based on a ramdom

sample of five customers.

a) what is the probability of exactly 4 customer are very satisfied?

b)more than 8 customers are very satisfied?

c) less than 7 customers are very satisfied?

d) suppose that of nine customers selected, four responded that they are very satisfied. What conclusions can be drawn about the sample

Answer 1

(here please revert if it is a sample of 9 people or 5 ; I am considering 9 on basis of part d)

a)

probability of exactly 4 customer are very satisfied =P(X=4)=⁹C₄(0.85)⁴(0.15)⁵ =0.004995

b)

more than 8 customers are very satisfied =P(X>8)=P(X=9)=⁹C₉(0.85)⁹(0.15)⁰ =0.231617

c)

less than 7 customers are very satisfied =P(X<7)=1-P(X>=7)=1-P(X=7)-P(X=8)-P(X=9)

=1-⁹C₇(0.85)⁷(0.15)² -⁹C₈(0.85)⁸(0.15)¹ -⁹C₉(0.85)⁹(0.15)⁰ =0.140853

d)

here as probability of 4 or less to be satsfied=P(X<=4)=0.005629

as probability of this event is signficantly low ; we can conclude that there is a chance that claim made by hotel is incorrect and the satisfction level might be lower then claimed