Let denote the probability that a randomly sampled individual in some population votedConservative in the last General Election. In a particular type of 'randomised response'experiment, each of a random sample of individuals from this population responds 'True' or'False' to one of the following two statements.(a) I voted Conservative at the last General Election.(b) I did not vote Conservative at the last General Election.A randomising device is used to ensure that the probabilities of responding to (a) and (b) are pand 1-p respectively, where p is known and 0

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Answered: Let 0 denote the probability that a…

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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Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 300 times and got 122 heads. We wish to find how significant is this evidence against equal probabilities. What is the sample proportion of heads? Round to 3 places. Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different?Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test? H0: p = 0.5H0: p ≠ 0.5 H0: p = 0.5H0: p > 0.5 H0: p = 0.5H0: p < 0.5 H0: p ≠ 0.5H0: p = 0.5 Compute the z test statistic.z = Round to 2 places.
In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal. You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent eight shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of eight shark attacks. So, what is the probability that five or more of the eight shark attacks are nonfatal? (Round your answer to three decimal places.)
A pair of dice is rolled, and the larger of the two numbers showing is recorded. Find the expected value of this experiment.
(c) Five chocolate biscuits are taken at random from a packet of 11 biscuits and inspected as a quality assurance test in a factory. The packet is rejected if more than 1 biscuit is found to have a fault which makes the biscuit of poor quality. If there are actually 3 poor quality biscuits in a packet currently being inspected, find the probability that this packet is accepted.
Q. 1 Suppose that 4.5% of all adults over 50 have cancer. A certain physician correctly diagnoses 94% of all adults over 50 with cancer as having the disease and incorrectly diagnoses 4% of all adults over 50 without cancer as having the disease. (i) Draw a tree diagram and label it with appropriate probabilities. (ii) Find the probability that a randomly-selected adult over 50 is diagnosed as not having cancer. (iii) Find the probability that a randomly-selected adult over 50 actually has cancer, given that he/she is diagnosed as not having cancer.
In a survey, 45% of the interviewees are of age below 30, 30% are between 30 and 50, and 25% are above 50. 90% of the interviewees aged below 30, 60% of the interviewees aged between 30 and 50, and 70% of the interviewees aged above 50 can swim. (a) If a randomly selected interviewee can swim, find the probability that his/her age is between 30 and 50. (b) If a randomly selected interviewee cannot swim, find the probability that his/her age is below 30.
A recent survey of post-secondary education students in Canada revealed that 76% are confident in their ability to manage their finances.You are to randomly pick 30 post-secondary education students across the country, and ask each the following question: Are you confident in your ability to manage your finances? You have defined the random variable X to represent the number, out of 30 post-secondary students chosen, who respond YES.(a) What is the probability that 22 of these post-secondary students respond YES?P(X=22)= _________(use four decimals in your answer) (b) What is the probability that between 14 and 20 of these students will respond YES?P(14≤X≤20)=_________(use four decimals in your answer) (c) How many of the 30 post-secondary students would you expect to respond YES? Find the standard deviation as well.E(X)=μX=_________(use two decimals in your answer) SD(X)=σX=_________ (use two decimals in your answer)

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