1. A traffic study shows that 90% of motor vehicles that come to a stop for a stop signal at a certain intersection have to wait at least 15 second before proceeding. Find the mean of the distribution of the number of motor vehicles among 10 randomly selected motor vehicles that come to this stop signal and have to wait at least 15 seconds before proceeding.
(a) by looking up the probabilities in Table I and then using the formula the defines the mean of a probability distribution:
(b) by using the special formula for the mean of the binomial distribution.
2. The probabilities that there will be 0,1,2,3,4, or 5 fires caused by lighting during a summer storm are as follows:
Number of fires caused by lightning
0, 1, 2, 3, 4, 5,
Probability
0.449, 0.360, 0.144, 0.038, 0.008, 0.001
3. A student answers the 144 questions on a true-false test by flipping a balanced coin.
(a) Use the special formulas for the mean and the standard deviation of the binomial distribution to find the values of μ and σ for the distribution of the number of correct answers that he or she will get.
(b) According to Chebyshev's theorem, what can we assert with a probability of at least 0.96 about the number of correct answers that he or she will get?
4. The number of dinners served at a restaurant each evening is a random variable with μ =50 and σ = 10. What does Chebyshev's theorem with k =3 tell us about the number of CDs sold each day?