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6. Tina Fey goes trick-or-treating the night of Halloween dressed as Sarah Palin. She visits homes in her neighborhood to collect candy, but only receives candy, naturally, when the door is answered and the family still has a piece of candy to give away. Upon knocking, the probability of the door being answered is 3/4, and the probability that the home still has candy is 2/3. Assume that the events “Door answered” and “candy remaining” are independent and also that the outcomes at each home are independent. Also assume that each home gives away at most a single piece of candy.
(a) Determine the probability that Tina receives her first piece of candy at the third house she visits.
(b) Given that she has received exactly four pieces of candy from the first eight houses, determine the conditional probability that Tina will receive her fifth piece of candy at the eleventh house.
A store contains 1 pair of boots with each of the following colors are black, chocolate and yellow. Each pair is put together in a particular place. You enter into the dark store and pick randomly the boot without looking at it. Then, you replace it with another boots. What is the probability that you will choose the black pair of boots both times?
5. A coin is tossed 400 times. Use the normal curve approximation to find the probability of obtaining
(a) between 185 and 210 heads inclusive;
(b) exactly 205 heads;
(c) fewer than 176 or more than 227 heads
How many strings can be formed in the length of 5 strings from the word DISCRETE?
4. The heights of 1000 students are normally distributed with a mean of 175 centimeters and a standard deviation of 7 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights
(a) less than 160.0 centimeters?
(b) between 171.5 and 182.0 centimeters inclusive?
(c) equal to 175.0 centimeters?
(d) greater than or equal to 188.0 centimeters?
3. A production process produces electronic component parts. It is presumed that the probability of a defective part is 0.01. During a test of this presumption, 600 parts are sampled randomly and 18 defectives are observed.
(a) What is your response to the presumption that the process is 1% defective? Be sure that a computed probability accompanies your comment.
(b) Under the presumption of a 1% defective process, what is the probability that only 3 parts will be found defective?
(c) Do parts (a) and (b) again using the Poisson approximation.
Evaluate ∫C (x + 2y) ds, where C is the curve defined by y = √(4 − x2), for x ∈ [0, 1].
The lengths (in minutes) of a random selection of popular children’s animated films are
listed below. Estimate the true mean length of all children’s animated films with 95%
confidence.
90 84 83 91 75 88 78 96 78 79 77
Given r1 = 3i − 4j + 3k, r2 = 5i + 3j − 6k, r3 = 2i + 7j + 3k and r4 = 4i + 3j + 5k.
Find the scalars a, b and c such that r4 = ar1 + br2 + cr3
2. Changes in airport procedures require considerable planning. Arrival rates of aircraft are important factors that must be taken into account. Suppose small aircraft arrive at a certain airport, according to a Poisson process, at the rate of 5 per hour. Thus, the Poisson parameter for arrivals over a period of hours is μ = 5t.
(a) What is the probability that exactly 4 small aircraft arrive during a 1-hour period?
(b) What is the probability that at least 4 arrive during a 1-hour period?
(c) If we define a working day as 12 hours, what is the probability that at least 75 small aircraft arrive during a working day?
#333702 on Dec 2022