In: Statistics and Probability

Each airline passenger and his luggage must be checked for security. Suppose that at Gotham City Airport, 3.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for security, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 4.2 passengers per minute, where the time to check a passenger is also exponentially distributed. Under the assumption that the airport has only one checkpoint, answer the following questions.

What is the probability that a passenger will have to wait before being checked for weapons? If needed, round your answer to one decimal digit.

On average, how many passengers are waiting in line to enter the checkpoint? If needed, round your answer to one decimal digit.

On average, how long will a passenger spend at the checkpoint (including waiting time in line)? If needed, round your answer to one decimal digit.

Given

= 3.6

= 4.2

The probability that a passenger will have to wait before being checked for weapons

= 3.6/4.2

= 0.857 ~ **0.8 (Round to one decimal place)**

On average, how many passengers are waiting in line to enter the checkpoint

On average, how long will a passenger spend at the checkpoint (including waiting time in line)

Average time at checkpoint W = Expected no.of customers (L) /

customers or passengers

Suppose that the demand and supply schedules for rental
apartments in the city of Gotham are as given in the table
below.
Monthly Rent $: 3,000 2,500 2,000 1,500 1,000
Apartments Demanded: 10,000 12,500 15,000 17,500 20,000
Apartments Supplied: 15,000 12,500 10,000 7,500 5,000
a. What is the market equilibrium rental price per month and the
market equilibrium number of apartments demanded and supplied?
Market equilibrium rental price is: _____ (per month). Market
equilibrium quantity is:_____ (apartments).
b. If the...

Airlines now charge passengers a fee for each piece of checked luggage, but they do not charge for carry- on luggage brought onto the plane. If overhead luggage containers fill up, the airline then checks luggage for free at the gate. Describe the effects of this system on the number and size of carry- ons brought onto the plane and the efficiency of the allocation of overhead space.

All airport passengers at the Capital City Airport must pass
through a security screening area before proceeding to the boarding
area. The airport has three screening stations available, and the
facility managers must decide how many to open at any particular
time. The average time for processing one passenger at each
screening station is 0.5 minutes. On Saturday morning the arrival
rate is 3.3 passengers per minute. Assume that processing times at
each screening station follow an exponential distribution and...

Suppose the City purchases five sidewalk plows worth $20,000
each to be used over 10 years. Determine the annual payments the
City is responsible for if the interest rate is constant at 3%.
Suppose the benefits of having cleared sidewalks in the
neighbourhood these snowplows will be used are estimated at $20,000
each winter, and the annual operating costs are $500 per plow,
should the City make this investment? Show your work.

Suppose the City purchases five sidewalk plows worth $20,000
each to be used over 10 years. Determine the annual payments the
City is responsible for if the interest rate is constant at 3%.
Suppose the benefits of having cleared sidewalks in the
neighbourhood these snowplows will be used are estimated at $20,000
each winter, and the annual operating costs are $500 per plow,
should the City make this investment? Show your work.

A basketball player makes 60% of his shots from the free throw
line. Suppose that each of his shots can be considered independent
and that he throws 4 shots. Let X = the number of shots that he
makes. What is the probability that he makes 1 shot?

A basketball player makes 40% of his shots from the free throw
line. Suppose that each of his shots can be considered independent
and that he takes 3 shots. Let X = the number of shots that he
makes. What is the standard deviation for X? 0.849 0.72 1.2 0.4

A basketball player makes 60% of his shots from the free throw
line. Suppose that each of his shots can be considered independent
and that he takes 4 shots. Let X = the number of shots that he
makes. What is the probability that he makes all 4 shots?

A basketball player makes 60% of his shots from the free throw
line. Suppose that each of his shots can be considered independent
and that he takes 4 shots. Let X = the number of shots that he
makes. What is the probability that he makes 3 shots?

Your father is 50 years old and will retire in 10 years. He
expects to live for 25 years after he retires, until he is 85. He
wants a fixed retirement income that has the same purchasing power
at the time he retires as $60,000 has today. (The real value of his
retirement income will decline annually after he retires.) Hisretirement income will begin the day he retires, 10 years
from today, at which time he will receive 24 additional...

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