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Discipline Statistics

Assignment type : Other types

Description

IHP 525 Module Three Problem Set

- What is the probability of being born on:
- a) February 28?
- b) February 29?
- c) February 28 or February 29?
- A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving 5 or more years. Let us assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.
- A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (about 1.8×10-8). There are no other prizes, so the probability of winning nothing = 1 – (1.8×10-8) = 0.999999982. The probability model is:

Winnings (X) 0 $10 x 106

P(X = xi) 0.999999982 1.8 x 10-8

- a) What is the expected value of a lottery ticket?
- b) Fifty-five million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?
- Suppose a population has 26 members identified with the letters A through Z.
- a) You select one individual at random from this population. What is the probability of selecting individual A?
- b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and then take a second random draw. What is the probability of drawing person A on the second draw?
- c) Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person A on the second draw?
- Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?
- What is the complement of an event?
- Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve” depicts the probability density function for accidents along this stretch:
- a) What is the probability that an accident occurred in the first mile along this stretch of highway?
- b) What is the probability that an accident did not occur in the first mile?
- c) What is the probability that an accident occurred between miles 2.5 and 4?
- Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.
- a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?
- b) If we randomly select two women from the population who then become pregnant, what is the probability that the first woman’s child will be a boy and the second woman’s child will be a boy?
- c) If we randomly select two women from the population who then become pregnant, what is the probability that both children will be boys given that at least one child is a boy?
- Explain the difference between mutually exclusive and independent events.
- Suppose a screening test has a sensitivity of 0.80 and a false-positive rate of 0.02. The test is used on a population that has a disease prevalence of 0.007. Find the probability of having the disease given a positive test result.

Format MLA

Academic Level: –

Volume of 2 pages (550 words)

Type of service: Custom writing