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Consider the group of all people that purchased a car in 2015. Suppose that 78% of these people requested anautomatic transmission, 42% requested a satellite radio, and 27% requested both of these features. Let Arepresent the event that a randomly chosen person from this group requested an automatic transmission, and Rbe the event that they requested a satellite radio. NOTE: In parts (A) - (D) you must first express eachprobability in terms of the events A and R.
(a) What is the probability a randomly chosen person in this group requested at least one of these two features?
(b) What proportion of the people in this group requested neither feature?
(c) What proportion of the people in this group requested an automatic transmission but did not request asatellite radio?
(d) If a person in this group requested an automatic transmission, what is the probability that they alsorequested a satellite radio?
Determine how large a sample would be necessary to estimate the population proportion with a margin of error of .05 at 95% confidence
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