1.1 What are the 95% condence limits on the variance in the first example above '? 1.2 YWhat are the 95 '35: condence limits on the mean if you (wrongly )use the 2 statistic in the rst example '5' 1.3 In a composite of 10 volcanoes the average mondily mean temperature anomaly three months after the eruption is 05 C colder than the monthly mean temperature anomaly one month before the eruption . The standard deviation of the monthly anomalies is 2.0'C. Is this result signicant '3 1.4 The average snowfall at Stevens Pass is 415 inches . This has a standard deviation of 100 inches and is based on 30 yearly observations . What are the 99% condence limits on the true mean ? 1.5 Annual mean precipitation in Seattle averages 894 mm ,with a standard deviation of 182 mm over a sample of 111 years . The 20 years from 1920 -1939 had an average of 785mm and a standard deviation of 113mm . Were the 2015 and 30 '5 different from the overall record '5' 1.6 Of swordsh taken by the Harman Baden ,0593 have cancerous lesions . If the sh has cancerous lesions 90% also have high levels of PCP . If the sh do not have lesions .309": nonetheless have high PCP . Use Bayes theorem to estimate how many of the sh with high PCP have lesions . Also .what is the probability that a swordfish has high PCP a 1.7 A student takes a 20-question multiple -choice exam where every question has 5 choices . Some of the answers she knows from study ,some she guesses . If the conditional probability mat she knows the answer =given that she answered it correctly , is 0.93 , for how many of the questions did she know the answer '9 1.3 An earthquake forecaster forecasts 20 earthquakes . How many of these forecasts must be successes in order to pass a 95% condence that the forecaster has nonzero skill ? What percentage is this? Compare to the case of 200 forecasts given above . 1.9 Historically ,rnajor midwinter warmings of the Northern Hemisphere stratosphere occur every other year (Lathe probability of getting one in any year is p=05). During the decade of the 1990 '5: seven successive years without major warmings occurred . What is the probability of this event occurring by chance ? What if it was not seven consecutive non -warming years , but merely 7" out of '10 in any order '1 What is the probability of getting 7 or more warmingless winters out of 10'? 1.10 You are a contestant on The Price is Right . Monte Hall shows you three doors . Behind one door is a Tesla Roadster . Behind the other two doors are goats . After you choose your door ,but before it is opened ,Monte opens another door to reveal a goat. He offers you the opportunity to switch to the other unopened door . Should you switch '5' 1What is the probability that your first choice is the car\".J What is the probability that the alternative offered is the car? You can assume that Monte is
