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# Michle Hibon works as a tutor for the Applied Statistics course two hours per day, four days a week. On average, about 6 students per hour come to...

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תיב ליגרת 2 1. Michèle Hibon works as a tutor for the Applied Statistics course two hours per day, four days a week. On average, about 6 students per hour come to see her, and the arrivals appear to be independent and stationary (occur at a stable rate). Twenty minutes after the tutoring hours begin one day, Michèle wants to take a coffee break for 15 minutes but doesn’t want to miss any students who might come to see her. So, she wonders what are the chances than no students will arrive during the next 15 minutes. Find this probability (a) if two students arrived in the past ten minutes, (b) if no students have come in to see her yet on this particular day. 2. Alkalinity of river water. The alkalinity level of water specimens collected from the Han river in Seoul, Korea, has a mean of 50 milligrams per liter and a standard deviation of 3.2 milligrams per liter. Assume the distribution of alkalinity levels is approximately normal and find the probability that a water specimen collected from the river has and alkalinity level: a. exceeding 45 milligrams per liter b. bellow 55 milligrams per liter c. between 51 and 52 milligrams per liter. 3. Let Y be a negative binomial random variable with parameters r and p. Then it can be shown that W=Y-r is also a negative binomial random variable, where W represents the number of failures before the rth success is observed. Use the facts that 2 2 2 2 ( ) and show that E(W)= and y w r rq EY p p to rq rq p p σ σ = = = 4. Color as body orientation clue. To compensate for disorientation in zero gravity, astronauts rely heavily on visual information to establish a top- down orientation. The potential of using color brightness as a body orientation clue was studied in Human factors (Dec.1988) . Ninety college students, reclining on their backs in the dark, were disorientated when positioned on a rotating platform under a slowly rotating disk that blocked their field of vision. The subjects were asked to say ''stop'' when they felt as if they were right –side up. The position of the brightness pattern on the disk in relation to each student's body orientation was the recorded. Subjects selected only three disk brightness patterns as subjective vertical clues: (1) brighter side up, (2) darker side up, (3) brighter and darker side aligned on either side of the subject's heads. Based on the study results, the probability of subjects selecting the three disk orientation are 0.65, 0.15 and 0.20 respectively. Suppose n=8 subjects perform and similar experiment.
a. What is the probability that all eight subjects select the brighter side-up disk orientation? b. What is the probability that for subject select the brighter side-up orientation, three selects the darker side up orientation, and one selects the aligned orientation. c. On average, how many of the eight subjects will select the brighter-side orientation.

As our variable W=Y-r so variance... View the full answer

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