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1. * (Distribution of Maximum). Suppose n numbers are drawn at random from f1; 2; ··· ;N g. What is the probability that the largest number drawn is a specified number k if sampling is (a) with replacement; (b) without replacement?
2. * (Poisson Approximation). One hundred people will each toss a fair coin 200 times. Approximate the probability that at least 10 of the 100 people would have obtained exactly 100 heads and 100 tails.
3. * (A Design Problem). You are allowed to choose a number n and then toss a fair coin ntimes. You will get a prize if you can get either seven or nine heads. What is your best choice of the numbern?
4. * (A Novel Way to Give a Test). A student takes a five-answer multiple-choice oral test. His grade is determined by the number of questions re- quired in order for him to get five correct answers. A grade of A is given if he requires only five questions; a grade of B is given if he requires six or seven ques- tions; a grade of C is given if he requires eight or nine questions; and he fails otherwise.
Suppose the student guesses independently at random on each question. What is his most likely grade?
In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms. Using a significance level of .01, test the claim that more than half of all those using the drug experienced relief.
what does it mean to say that your score on test one in statistics was in the 90th percentile?
When a large shipment of alternators is received at the plant, 100 are tested and if more than two are nonconforming, the shipment is returned to the alternator manufacturer. What is the probability of returning a shipment?
to run a successful business you need to learn about your customers your competitors and your industry. market research
Determine probability of waiting less than 12 minutes between successive speeders. By using cumulative distribution function of X.
A statistics profressor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 60.0 minutes. Find the probability that a given class period runs great than 50.5 minutes.
Covariates included self-reported lifetime history of hypertension, gallbladder disease, and non-estrogen drug use.
suppose x and y are independent. let x have the mean 3 and y have the mean 2. find the covariance of xy and
Define the null hypothesis. If the null hypothesis is rejected then? Read the Z statistic from the normal distribution table:
1 according to the american cancer society melanoma a form of skin cancer kills 15 of americans who suffer from the
Three couples attend a dinner. Each of the six people chooses randomly a seat at a round table. What is the probability that no couple sits together?
A gardner plants 12 flowers. It is perdicted that on an average, 15% of the flowers planted will die during the first winter. Using the information above, please answer the following questions:
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