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Probability - Statistics - Quiz, Exercises of Statistics

This lecture is from Statistics. Key important points are: Probability, Data File Energy, Capita Energy Consumption, Standard Deviation, Energy Consumption, Study Consumer Behavior, Shopping for Clothing, Box of Nine Gloves, Box Without Replacement, Right Handed

Typology: Exercises

2012/2013

Uploaded on 01/29/2013

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Question: A The data file energy contains the per capita energy consumption, in
Kilowatt hours, for each of the 50 states and the District of Columbia during
recent year.
a. Compute the mean, variance, and standard deviation for the population.
b. What proportion of these states has average per-capita energy consumption
within μ +σ, μ – σ, within μ +2σ, μ – 2σ, and within μ +3σ, μ – 3σ? Using
Chebyshev Rule.
c. compare and contrast your result based on empirical rule.
Question 1. A sample of 500 respondents was selected in a large metropolitan area
to study consumer behavior. Among the questions asked was “do you enjoy
shopping for clothing?” Of 240 males, 136 answers yes. Of 260 females 224
answers yes. Construct a contingency table to evaluate the probabilities. What is
the probability that a respondent chosen at random
a. enjoy shopping for clothing?
b. is a female and enjoys shopping for clothing?
c. is a female or enjoys shopping for clothing?
d. is a male or a female?
Question 2. A box of nine gloves contains two left handed gloves and seven right
handed gloves.
a. If two gloves are randomly selected from the box without replacement, what is
the probability that both the gloves selected will be right handed?
b. If two gloves are randomly selected from the box with replacement, what is the
probability there will be one right handed glove and one left handed glove
selected?
c. If three gloves are randomly selected with replacement, what is the probability
that all three will be left handed?
d. If you are sampling with replacement what would be the answer to (a) and (b).
Question 3. An advertising executive is studying television viewing habits of
married men and women during prime time hours. Based on past viewing records,
the executive has determined that during prime time, husbands are watching
television 60% of the time. When the husband is watching television, 40% of the
time wife is also watching. When husband is not watching television, 30% of the
time the wife is watching television. Find the probability that
a. if wife is watching television, the husband is also watching.
b. the wife is watching television in prime time.
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Question: A The data file energy contains the per capita energy consumption, in Kilowatt hours, for each of the 50 states and the District of Columbia during recent year. a. Compute the mean, variance, and standard deviation for the population. b. What proportion of these states has average per-capita energy consumption within μ +σ, μ – σ, within μ +2σ, μ – 2σ, and within μ +3σ, μ – 3σ? Using Chebyshev Rule. c. compare and contrast your result based on empirical rule.

Question 1. A sample of 500 respondents was selected in a large metropolitan area to study consumer behavior. Among the questions asked was “do you enjoy shopping for clothing?” Of 240 males, 136 answers yes. Of 260 females 224 answers yes. Construct a contingency table to evaluate the probabilities. What is the probability that a respondent chosen at random a. enjoy shopping for clothing? b. is a female and enjoys shopping for clothing? c. is a female or enjoys shopping for clothing? d. is a male or a female?

Question 2. A box of nine gloves contains two left handed gloves and seven right handed gloves. a. If two gloves are randomly selected from the box without replacement, what is the probability that both the gloves selected will be right handed? b. If two gloves are randomly selected from the box with replacement, what is the probability there will be one right handed glove and one left handed glove selected? c. If three gloves are randomly selected with replacement, what is the probability that all three will be left handed? d. If you are sampling with replacement what would be the answer to (a) and (b).

Question 3. An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on past viewing records, the executive has determined that during prime time, husbands are watching television 60% of the time. When the husband is watching television, 40% of the time wife is also watching. When husband is not watching television, 30% of the time the wife is watching television. Find the probability that a. if wife is watching television, the husband is also watching. b. the wife is watching television in prime time.

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Question 4. ELISA is the most common type of screening test for detecting the HIV virus. A positive result from an ELISA indicated that the HIV virus is present. For most populations, ELISA has a high degree of sensitivity and specificity. Suppose that the probability that is person is infected with the HIV virus for a certain population is 0.015. If the HIV virus is actually present, the probability that the ELISA test will give a positive result, the probability of a positive result from an ELISA is 0.01. If the ELISA has given a positive result, use Bay’s theorem to find the probability that the HIV Virus is actually present.

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