4. City officials estimate that a dangerous intersection in the city has 0.75 accidents per month. Let be the number of accidents that occur at this intersection over the next two months. a) What probability distribution can you use to model ? XX b) Calculate the probability that are at most three accidents occur at this intersection in the next two months. Write out the equation you need with numbers substituted but solve using R. Copy/paste your R code here, with the answer. 5. During a tight job market, recruiters have noticed that graduating seniors with an intermediate proficiency in a second language have a higher probability of getting a first interview following a screening call when seeking their first job out of college. For students with one language, the probability of getting a first interview following a screening call is 0.25, whereas for graduating seniors with a second language the probability is 0.35. Let be the number of screening calls a graduating senior with an intermediate proficiency in a second language must go through before getting their first interview. XX a) Name a probability distribution that you could use to find probabilities of X. Do not forget to include values of any parameters. b) On average, how many screening calls must a graduating senior with an intermediate proficiency in a second language go through before getting their first interview? c) What is the exact probability that a graduating senior with an intermediate proficiency in a second language must have at most three screening calls before getting their first interview? Write down the formula you would use with numbers substituted but use R to calculate the answer. Copy and paste your R code here with the answer. 6. Let X be a random variable that denotes the number of tails in a set of 25 tosses. a) What is the sample space for ? b) Assume that the coin is unfair with Assuming independent toss outcomes, what probability distribution can you use to model ? Make sure to name the distribution and the values of any parameters. PRTT = 0.35. c) What are and based on the distribution named in part (b) above? Interpret these numbers. XX d) What is the exact probability that in any given case? Write down the formula you would use with numbers substituted but use R to calculate the answer. Copy and paste your R code here with the answer. XX> 5 e) Explain why the number of heads out in a set of 25 tosses can be modeled as a binomial random variable with parameters and 7. A hung jury is one that is unable to come to a unanimous decision regarding the guilt of the defendant. Suppose that there is a pool of 40 potential jurors, but 3 of the 40 potential jurors would never be willing to convict, regardless of the evidence presented. a) Name a probability distribution that you could use to find probabilities of X. Do not forget to include values of any parameters. b) What is the probability that the trial will result in a hung jury, regardless of the evidence, if the jury consists of 12 randomly selected jurors? Write out the equation you need with numbers substituted but solve using R. Copy/paste your R code here, with the
