Italia Jackets

statistics-multinomial probability and hypergeometric distribution?

1. The probabilities are 0.25, 0.40, and 0.35 that an 18-wheel truck will have no violations, 1 violation, or 2 or more violations when it is given a safety inspection. If 8 trucks are inspected, find the probability that 3 will have no violations, 2 will have 1 violation, and 3 will have 2 or more violations. 2. A die is rolled 4 times. Find the probability of 2 1s, one 2, and one 3. 3. A recent study of robberies for certain geographic region showed an average of one robbery per 20 000 people. In a city of 80 000 people, find the probability of the following: a. No robberies b. One robbery c.2 robberies d. 3 or more robberies 4. In a 400-page manuscript, there are 200 randomly distributed misprints. If a page is selected, find the probability that it has one misprint. 5. A telephone-soliciting company obtains an average of 5 orders per 1000 solicitations. If the company reaches 250 potential customers, find the probability of obtaining at least 2 orders. 6. If 90% of all people between the ages of 30 and 50 drive a car, find these probabilities for a sample of 20 people in that age group. a. Exactly 20 drive a car b. At least 15 drive a car c. At most 15 drive a car 7. If 5 cards are drawn from a deck, find the probability that 2 will be hearts. 8. A board of directors consists of 7 men and 5 women. If a slate of 3 officers is selected, find these probabilities. a. Exactly 2 are men b. All 3 are women c. Exactly 2 are women 9. There are 48 raincoats for sale at a local men's clothing store. 12 are black. If 6 raincoats are selected to be marked down, find the probability that exactly 3 will be black. 10. A youth group has 8 boys and 6 girls. If a slate of 4 officers is selected, find the probability that exactly a. 3 are girls b. 2 are girls c. 4 are boys

Public Comments

1. 1 ANSWER: PROBABILITY = 21% of 3 with no violations. Why??? BINOMIAL DISTRIBUTION, POPULATION PROPORTION n = NUMBER OF TRIALS [ 8] (sample size) k = NUMBER OF SUCCESSES [3] (from 0 up to and including k NUMBER OF SUCCESSES) p = POPULATION PROPORTION [25%] significant digits2 COMPUTATION OF BINOMIAL PROPORTION: P(k ≤ 3) = n!/[k!*(n - k)!] * p^k * (1 - p)^(n - k) = 0.21 Binomial Probability Computational Example for NUMBER OF TRIALS = 5, NUMBER OF SUCCESSES = 2, POPULATION PROPORTION = 0.10 P(k ≤ 2) = {5!/[2!*(5 - 2)!] * 0.1^2 * (1 - 0.1)^(5 - 2) + 5!/[1!*(5 - 1)!] * 0.1^1 * (1 - 0.1)^(5 - 1) + 5!/[0!*(5 - 0)!] * 0.1^0 * (1 - 0.1)^(5 - 0)} ALTERNATIVE COMPUTATION USING EXCEL: "Look-up" value of PROBABILITY = 0.21 = BINOMDIST ( 3 , 8 , 25/100 , TRUE ) "Using Excel function: BINOMDIST(number_s, trials, probability_s, cumulative) Number_s is the number of successes in trials. [ 8 ] Trials is the number of independent trials. [ 3 ] Probability_s is the probability of success on each trial. [25]" Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes. ANSWER: PROBABILITY = 21% of exactly 2 with one violation. ANSWER: PROBABILITY = 72% of 2 or more with three violations.