For the past 111 years, a certain state suffered 23 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d). (a) What is the probability that the state will not be hit by any major hurricanes in a single year? The probability is. (Round to four decimal places as needed.) (b) What is the probability that the state will be hit by at least one major hurricane in a single year? The probability is (Round to four decimal places as needed.) Is this unusual? O No O Yes (c) What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened several years ago? The probability is. (Round to four decimal places as needed.) Does this indicate that the hurricane season several years ago in this state was unusual? O No O Yes (d) What is the probability that the state will be hit by at least two major hurricanes in a single year, as happened last year? The probability is (Round to four decimal places as needed.) Does this indicate that the hurricane season this year in this state was unusual?

(first part of question is attached) (e) What is the probability that the sample proportion of students of adults living with parents or other relatives is higher than 0.3? (f) What is the probability that the sample proportion of adults living alone is between 0.1 and 0.15?

2. Give the probability generating function for an offspring distribution in which an individual either dies, with probability 1- p, or gives birth to three children, with probability p, Also find the mean and variance of the number of children in the fourth generation.

The bottom panel of figure 1 (p. 311) shows the probability histogram for the total number of spots when a pair of dice are rolled. (a) The chance that the total number of spots will be between 7 and 10 (inclusive) equals the area under the histogram between ___and ___ (b) The chance that the total number of spots will be 7 equals the area under the histogram between ___ and ____

K The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. Complete parts (a) through (c) below. Click the icon to view the data for fatal crashes in 2016. (a) Among fatal crashes in unknown weather conditions, what is the probability that a randomly selected fatal crash occurs when it is dawn/dusk? The probability that a randomly selected fatal crash in unknown weather conditions occurs when it is dawn/dusk is approximately. (Round to three decimal places as needed.) Data table Weather Daylight Dark, but Lighted 5875 497 51 54 255 Normal Rain Snow/Sleet Other Unknown 14,307 875 219 125 810 (...) Dark 8151 681 156 220 548 Dawn/Dusk Other 1183 87 40 71 65 8 2 9 133 X