1-A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. For 20 mornings, what is the probability that the light is green on more than four days?

2-The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter. What is the probability that there is one flaw in 10 square meters of cloth?

3-The probability that a person, living a certain city, owns a dog is estimated to be 0,3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.

4-A random variable X has the following probability distribution:

f(x)= {█(x+1 x=0,1,2,3,..,[email protected] elsewhere )┤

Find the mean and variance by using moment generating function.

5-Seventy new jobs are opening up at an automobile manufacturing plant, but 1000 applicants show up for the 70 positions. To select the best 70 from among the applicants, the company gives a test that covers mechanical skill, manual dexterity and mathematical ability. The mean grade on this test turns out to be 60 and the scores have a standard deviation 6. Can a person who has an 84 score count on getting one of the jobs? (HINT: use Chebyschev’s theorem) Assume that the distribution is symmetric about the mean.