University:
University of Houston
Course:
MATH 1313 | Linear Algebra
Academic year:

2022
Views:

413

Pages:

4
Author:

Carina Watson

Page |2 Test #2 1. (2 points each) In each of the scenarios below, indicate whether the distribution of X is binomial, poisson, negative binomial (r >1), geometric, or neither. (a) Draw marbles from a bag containing 5 red marbles, 6 blue marbles and 4 green marbles without replacement until you get a blue marble. (b) Draw marbles from a bag containing 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble. (c) Draw 4 marbles, one at a time, from a bag containing 5 red marbles, 6 blue marbles and 4 green marbles with replacement and count the number of blue marbles. (d) Roll a pair of dice 10 times and count the number of times the sum is 6. (e) Roll a pair of dice until you get a sum of 6 on 4 of the rolls. (f) Twenty percent of all students at a college campus have more than two siblings. We want to determine how many students need to be interviewed before a student is found that has more than two siblings. 2. (Multiple Choice, 10 points) Suppose X ~ Bin ( n = 20, p = 0.4 ) Determine P(9 ≤ X ≤ 10). a) 0.4768 b) 0.1597 c) 0.2597 d) 0.2768 e) 0.3208 f) None of the above Math 3338: Probability Test #2 Page |7 8. The lifetime, in years, of a particular lcd television is known to be exponentially distributed with an expected lifetime of 20 years. (a) (7 points) Determine the probability that one of these lcd televisions lasts more than 30 years. (b) (7 points) A certain restaurant purchases 4 of these televisions. What is the probability that at least 2 of them are still working in 30 years. Math 3338: Probability Test #2 Page |5 6. (3 points each) Suppose that in a large metropolitan area, 85% of all households have cable tv. Consider selecting groups of five households, and let X be the number of households in this group that have cable tv. (a) Identify the distribution of X and any parameter(s) of this distribution. (b) What is the probability that exactly four of the five households have cable tv? (c) What is the probability that at most two of the households have cable tv? (d) Determine Var(X) (e) What is the probability that the actual number of households among the 5 selected that have cable tv is within 2 standard deviations of the expected number of households that have cable tv? Math 3338: Probability Test #2 Page |3 3. (Multiple Choice, 10 points) A manufacturer of matches randomly and independently puts 21 matches in each box of matches produced. Suppose it is known that 0.8% of the matches produced by this manufacturer are flawed. What is the probability that a matchbox from this manufacturer will contain one or fewer matches with a flaw? a) 0.006813 b) 0.9878 c) 0.9920 d) 0.1431 e) 0.8448 f) None of the above 4. (10 points) Suppose that the manufacturer in problem #3 above randomly chooses 30 boxes of matches from the next shipment to inspect for flaws. He will destroy the shipment if he finds more than 2 boxes of matches with more than 1 flaw. Determine the probability that he must destroy this shipment of matchboxes.