1) In testing a certain class of truck tire on rough terrain, it is found that 25% of the trucks fail the road test without a puncture. Of the following 15 trucks tested, find the probability that: a. 3 to 6 will have punctures. b. Less than 4 have punctures. C. More than 5 have punctures.

Exercise 2. At a certain intersection, an average of 3 traffic accidents occur per month. What is the probability that at any time, at this intersection: a. Did exactly 5 accidents occur? b. Did less than 3 accidents occur? C. Did at least 2 accidents occur?

Exercise 3. An engineer travels every day from his house to his office in the center of the city. The mean time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. If the distribution of travel times is assumed to be normally distributed. a. What is the probability that a trip will take at least half an hour? b. If the office opens at 9:00 am and he leaves his house at 8:45 am each day, what percentage of the time is he late for work? C. If he leaves his house at 8:45 am and coffee is served in the office from 8:50 am to 9:00 am, what is the probability that he will miss the coffee? d. Calculate the longest duration in which the slowest 15% of trips are found. me. Find the probability that 2 of the next 3 trips take at least half an hour.

Exercise 4. A bus arrives every 10 minutes at a stop. The waiting time for a particular individual is assumed to be a random variable with a continuous distribution. a. What is the probability that the individual waits more than 7 minutes? b. What is the probability that the individual waits between 2 and 7 minutes?

Exercise 5. The number of coffee liters per day, in which a machine located in the lobby of an airport serves, is between 7 and 10. The random variable is considered to have a uniform continuous distribution. Find the probability that on a given day the amount of coffee served by this machine is: a. At most 8.8 liters. b. More than 7.4 litres, but less than 9.5 litres. C. At least 8.5 liters.

Exercise 6. The heights of 1,000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. If 200 random samples of size 25 are drawn from this population and measurements are recorded to the nearest tenth of a centimeter, determine: a. The means and standard deviation of the sampling distribution. b. The number of sample means that fall between 172.5 and 175.8 centimeters. C. The number of sample means that fall below 172.0 centimeters.