The data in the following table show the association between cigar smoking and death from cancer for 133,053 men.​ Note: current cigar smoker means cigar smoker at time of death.                                      Died from Cancer    Did Not Die from Cancer Never smoked cigars          541                             119,955 Former cigar smoker           98                                6,749 Current cigar smoker         130                                5,580 (a)  If an individual is randomly selected from this​ study, what is the probability that he died from​ cancer? (b)  If an individual is randomly selected from this​ study, what is the probability that he was a current cigar​ smoker? (c)  If an individual is randomly selected from this​ study, what is the probability that he died from cancer and was a current cigar​ smoker? (d)  If an individual is randomly selected from this​ study, what is the probability that he died from cancer or was a current cigar​ smoker?

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3. Two board members were chosen at random from 12 candidates of which 8 were independent candidates. a. Determine the probability distribution for the number of independent candidates selected. b. Find the mean and the variance of the distribution of the number of independent candidates chosen as board members.

5. When flipping a penny or spinning a penny, is the probability of getting heads the same? Use the data in the table below with a 0.05 significance level to test the claim that the proportion of heads is the same with flipping as with spinning. Heads Tails 14,709 14,306 9197 11,225 Flipping Spinning

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What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Find the probability that a British nurse selected at random in 1851 would be 70 years of age or older. Round your answer to nearest thousandth.

A survey of property owners' opinions about a street-widening project was taken to determine if owners' opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next.     Opinion  Front Footage For Undecided Against  Under 45 feet 12 4 4  45-120 feet 35 5 30  Over 120 feet 3 2 5 What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?   Select one: a. 1.1 b. 3.9 c. 5.0 d. 5.5

The 2015 National Vital Statistics Report provides information on how the nearly four million live births that occurred in 2014 broke down by birth order. Choose at random a baby born in the United States in 2014. Baby's birth order Probability mean = 1 2 0.391 0.319 The few babies who were 9th or more in birth order are included in the "8" birth order group. In 2014, 39.1% of the nearly 4 million live births in the United States were to first-time mothers. 3 5 6 7 4 0.168 0.072 0.028 0.012 0.005 standard deviation = What are the properties of the sampling distribution of the proportion of births to first-time mothers in random samples of 500 births from 2014? (Enter your answer for the mean rounded to three decimal place and your answer for the standard deviation rounded to four decimal places.) 8 0.005

4. Michael is running for president. The proportion of voters who favor Michael is 0.8. A simple random sample of 100 voters is taken. Assume that n/N < 0.05.

a. What is the probability of seeing positive change? b. What is the probability of seeing positive change given that the tree is oak? c. Do the data suggest effect and tree type are independent events? yes or no