Suppose passengers arrive at the MTA train station following a Poisson distribution with parameter 9 and the unit of time 1 hour.

Next train will arrive either 1 hour from now or 2 hours from now, with a 50/50 probability.

i. E(train arrival time)

ii. E(number of people who will board the train)

iii. var(number of people who will board the train)

Up to 20% of Americans contract influenza each year. A sample of 400 randomly selected Americans is chosen and the number with influenza is recorded. Let X represent the number with influenza in the sample. What is the probability that, at most, 25% of the sample is observed to have influenza? How can I do this the easiest way on Ti-84? Can I use a button like Stats or Distr to make life easy?

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

a-2. Is this a discrete or a continuous probability distribution?

Discrete

Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

(b) What is the probability that at least 10 of these are from the second section? (Round your answer to four decimal places.)


(c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.)


(d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.)

(e) What are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.)

Please answer parts B, C, D, and E

A doctor is investigating the effect of a woman's age on the success of an IVF (in vitro fertilisation) procedure. She has randomly selected 10 women aged under 35 and 10 women aged at least 35. From hospital records she has obtained the following data, which record the numbers of eggs obtained from the women and the numbers that were fertilised during one IVF procedure. She wants to investigate the effect of the woman's age on the probability of an egg being successfully fertilised. She calls this probability the "fertilisation rate".

1. Carry out a suitable exploratory analysis to see whether the fertilisation rate might depend on the woman's age.

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 236 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

a-2. Is this a discrete or a continuous probability distribution?

Discrete

Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 232 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

1. a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

1. a-2. Is this a discrete or a continuous probability distribution?

• Discrete

• Continuous

1. b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

1. b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

3. Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 235 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

1. a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

1. a-2. Is this a discrete or a continuous probability distribution?

• Discrete

• Continuous

1. b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

1. b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

3. Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.

Click here for the Excel Data File

a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

a-2. Is this a discrete or a continuous probability distribution?

Discrete

Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

rev: 10_12_2018_QC_CS-142885

1. Suppose an individual considering purchasing health insurance has a 10% chance of developing a condition that costs $50,000 to treat. The individual has initial disposable income of $90,000 and is risk averse, with utility over final disposable income given by v ( I ) = sq root I.

a) What is the highest premium this individual is willing to pay for an insurance policy that reimburses them $50,000 if they need treatment? (20 points)

b) Now suppose that indiviudals may be either low risk (in which case the probability of developing the condition is 10%) or high risk (in which case the probability of developing the condition is 90%). If the insurance provider cannot tell which category a given individual falls into, what is a fair premium for a policy that pays out $50,000 if treatment is needed? (5 points)

c) Now suppose that although the insurance company cannot tell the individuals risk category, the individuals purchasing insurance know their own risk category. If the insurance company offers two policies: one which pays out $50,000 in the event that treatment is needed, with a premium of $25,000 and another which pays out $2,500 if treatment is needed, with a premium of $500, which policy would be chosen by high risk individuals and which policy would be chosen by low risk individuals? (10 points)