1. Strikes in a factory occur according to a Poisson process at a mean rate of 2 per year (we assume a year to be exactly 52 weeks). (a) Find the probability that there is exactly one strike in the first 4 weeks and exactly 3 strikes in the subsequent 13 weeks. (b) What is the probability that at least 2 strikes occur in 13 weeks? (c) How many strikes are expected to occur in 2 years?

Disregarding the possibility of a February 29 birthday, suppose a randomly selected individual is equally likely to have been born on any one of the other 365 days. (a) If 8 people are randomly selected, what is the probability that all have different birthdays? (Round your answer to three decimal places.) If 8 people are randomly selected, what is the probability that at least two have the same birthday? (Round your answer to three decimal places.) (b) With k replacing 8 in part (a), what is the smallest k for which there is at least a 50-50 chance that two or more people will have the same birthday? (c) If 8 people are randomly selected, what is the probability that either at least two have the same birthday or at least two have the same last three digits of their Social Se [Note: The article "Methods for Studying Coincidences"+ discusses problems of this type.] (Assume birthdays and the last three digits of Social Security numbers are ind- your answer to three decimal places.)

5. A new type of car tires is released on the market with rate of tire cracking: on average one crack every 2000km. (a) What is the probability that a randomly chosen tire will cover a distance of 500km without a single crack? (b) How many tires are expected to have two ore more cracks within a distance of 500km?

how do i solve parts A and B?

#24) a random sample of 15 heart rate monitors. If 20% of the heart rate monitors are defective in the series, what is the probability that between 5 and 8 (inclusive) heart rate monitors from this sample are defective?

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean u = 260 days and standard deviation o = 8 days. (a) What proportion of pregnancies lasts more than 272 days? (b) What proportion of pregnancies lasts between 248 and 266 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 256 days? (d) A "very preterm" baby is one whose gestation period is less than 242 days. Are very preterm babies unusual?

12.)The survival rate for trees planted at a particular landscaping company has been 83% in the past. (a) What is the probability that 9 of the next 12 trees planted will survive? (b) What is the probability that no more than 9 of the next 12 trees planted will survive? (c) What is the probability that at least 9 of the next 12 trees planted will survive? (d) What is the probability that 6 to 9 (at least 6 but no more than 9) of the next 12 trees survive? (e) How many of the next 12 trees planted would you expect to survive?