1. The probability of a student graduating from college in four years is 0.4. If 6 students are selected at random, find the probability that at least 1 of them will not graduate in 4 years?
2. A baseball team is having a 10 game home stand. If the probability that they win a game at home is 0.6, find the probability that they win between 5 and 8 games on this home stand.
3. According to Financial Executive (July/August 1993) disability causes 40% of all mortgage foreclosures. Given that a large lending institution audits 20 mortgage foreclosures, what is the probability that less than 8 eight foreclosures are due to a disability?
4. A coin is tossed four times. Find the mean, variance, and standard deviations of the number of heads that will be obtained.
5. A survey from Teenage Research Unlimited found that 30% of teenage consumers receive their spending money from part-time jobs. If five teenagers are selected at random, find the probability that at least three of them will have part-time jobs.
6. A book of 500 pages has 500 misprints. Using the Poisson distribution, estimate to three decimal places the probabilities that a given page contains:
a. Exactly 3 misprints?
b. More than 3 misprints?
7. A hire company has two lawnmowers, which it hires out by the day. A Poisson distribution with mean 1.5 may model the number of demands per day. In a period of 100 working days, how many times do you expect:
a. Neither lawnmower to be used?
b. Some requests for a lawnmower to be refused?