(a) Every working day, Alan reverses his car from his driveway on to the road in such a waythat there is a very small probability p that his car will be involved in a collision.(i) Show that the probability that there will be no collision in a five-day week is (1– p)³.(ii) State one assumption that is made in your answer above.(iii) Let p0.001. Check that the Poisson approximation can be used, and find theapproximate probability that Alan will avoid a collision in 500 working days. Roundyour answer to 4 decimal places.(b) Organisms are present in ballast water discharged from a ship according to a Poisson pro-cess with a concentration of 4 organisms per cubic meter. Find the probability that thenumber of organisms in 1.5 cubic meter of discharge exceeds its mean value by more thanone standard deviation. Round your answer to 4 decimal places.(c) The number of times that a person gets a cold in a given year is a Poisson random variablewith parameter A = 5. Suppose that a new supplement which has just been marketedreduces the Poisson parameter to A = 3 for 75% of the population. For the other 25% ofthe population, the supplement gives no significant reduction on the number of colds. If anindividual tries the supplement for a year and has 2 colds in that time, find the conditionalprobability that the supplement is beneficial for him or her. Round your answer to 4 decimalplaces.

(a)I GIVEN Alan reverses his car from his driveway in the road in such a way that there is a very…

(i) Show that the probability that there will be no collision in a five-day week is (1 – p)°. (ii) State one assumption that is made in your answer above. (iii) Let p = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that Alan will avoid a collision in 500 working days. Round

(i) Show that the probability that there will be no collision in a five-day week is (1 – p)°. (ii) State one assumption that is made in your answer above. (iii) Let p = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that Alan will avoid a collision in 500 working days. Round

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Everyday, James reverses his car from his driveway on to the road in such a way that there is a very small probability P that his car will be involved in a collision. ( i) Show that the probability that there will be no collision in a five-day week is (1−P)^5 and state one assumption that is made in your answer. (iii) Let P = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that James will avoid a collision in 500 days.
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Il fail within the first year. of 100 Christmas lights, there is a 0.01 chance that a given bulb will fail bulb fails, it does not affect the others). - large so we use Poisson approximation.
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
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2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ? 2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction? 2c) Using the previous results for lambda and continuity correction, find z, then graph and use your table to find φ table value of z Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.
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