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On February 27, 2013, the City Council of Cincinnati (OH) passed an ordinance requiring photoelectric smoke detectors in all rental properties. How- ever, over 5 years later, the city's fire department representatives are concerned that not all properties are adhering to the ordinance. Suppose the population proportion of rental properties in Cincinnati having photoelectric smoke detectors is 0.80 (i.e., 80 percent). (a) If a sample of 6 rental properties is selected at random, what is the probability at least 5 properties have photoelectric smoke detectors installed? (b) What three Bernoulli trial assumptions did you make in performing the calculation in part (a)? (c) Instead of sampling a fixed number of rental properties, suppose rental properties were inspected until the third one without photoelectric smoke detectors was found. Under the assumptions you outlined in part (b), please write precisely the distribution of the number of rental properties that would be inspected. Graph the side by side pdf and cdf plots to present the distribution with proper subtitles. (d) Calculate the probability that the number of rental properties inspected exceeds 10 until the third one was found without photoelectric smoke detectors. On February 27, 2013, the City Council of Cincinnati (OH) passed an ordinance requiring photoelectric smoke detectors in all rental properties. How- ever, over 5 years later, the city's fire department representatives are concerned that not all properties are adhering to the ordinance. Suppose the population proportion of rental properties in Cincinnati having photoelectric smoke detectors is 0.80 (i.e., 80 percent). (a) If a sample of 6 rental properties is selected at random, what is the probability at least 5 properties have photoelectric smoke detectors installed? (b) What three Bernoulli trial assumptions did you make in performing the calculation in part (a)? (c) Instead of sampling a fixed number of rental properties, suppose rental properties were inspected until the third one without photoelectric smoke detectors was found. Under the assumptions you outlined in part (b), please write precisely the distribution of the number of rental properties that would be inspected. Graph the side by side pdf and cdf plots to present the distribution with proper subtitles. (d) Calculate the probability that the number of rental properties inspected exceeds 10 until the third one was found without photoelectric smoke detectors