An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%.

Answer 1

Use the normal approximation to the binomial distribution.

mean = np
standard deviation = √npq

Therefore:
mean = .94n
standard deviation = √(n)(.94)(.06) = √(.0564n)

Using z-scores:
z = (x - mean)/sd
With the data:
1.645 = (160 - .94n)/√(.0564n)

Solve for n.

(Hint: Round answer to 165.)

Answer 2

Wouldn't you have to use the continuity correction factor if using the normal approximation to the binomial?

Answer 3

Create one week schedule. You have 5 members of management. Manager 1 is the Store Manager Isabela, Manager 2 is the Assistant Manager Madian, Manager 3 is another Assistant Manager Bryan, Manager 4 is Area Supervisor Violeta, Manager 5 is Front End Supervisor Virginia. Store Manager, and both Assistant Mangers can work 9 hours 30 minutes per day. Area Supervisor and Front End Supervisor can only work 8 hours per day. Each manager needs to be off 2 days per week. There needs to be at least 3 OR 4 (your choice) managers schedule per day. Morning shifts starts at 8:00am. Closing shift ends at 10:30pm with one manager closing per day. The store opens seven days per week.

Answer 4

Here is a possible schedule:

Monday:
- 8:00am-5:30pm: Isabela, Madian, Bryan
- 11:30am-8:00pm: Violeta, Virginia

Tuesday:
- 8:00am-5:30pm: Isabela, Madian, Virginia
- 11:30am-8:00pm: Bryan, Violeta

Wednesday:
- 8:00am-5:30pm: Isabela, Bryan, Virginia
- 11:30am-8:00pm: Madian, Violeta (closing)

Thursday:
- 8:00am-5:30pm: Isabela, Bryan, Violeta
- 11:30am-8:00pm: Madian, Virginia

Friday:
- 8:00am-5:30pm: Isabela, Madian, Virginia
- 11:30am-10:30pm: Bryan (closing), Violeta

Saturday:
- 8:00am-5:30pm: Isabela, Bryan, Virginia
- 11:30am-10:30pm: Madian (closing), Violeta

Sunday:
- 10:00am-7:30pm: Isabela, Madian, Bryan
- 10:30am-7:00pm: Violeta, Virginia (off)