Flashcards
Unit 7 - Discrete Distributions Test
Cards in this deck (20)
- 1According to a recent survey, 37 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. Let the random variable G represent the number of people selected to find one person who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?2.70
- 2—1.79
The expected value of B is the sum of the products of the number of books and their respective probabilities. In this case, 0(0.35)+1(0.20)+2(0.15)+3(0.10)+4(0.07)+5(0.08)+6(0.04)+7(0.01)=1.79. - 3A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at most 8 of the 9 participants will correctly identify the tap water?0.9980
- 4According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have not graduated from high school?binomialpdf(15, 0.19, 5)
- 5The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or more times when this coin is flipped 25 times?0.77
- 6In which of the following should the random variable X not be modeled with a geometric distribution?In a bag of 30 different colored candies, about 20% are red. One candy will be selected one at a time without replacement, and its color will be recorded. Let X represent the number of candies selected before red is selected.
This is not a geometric setting. The selections are not independent because of sampling without replacement from a small population. Therefore, the probability, p, will change with each selection. - 7A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards are shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. Let X represent the number of games that have been won out of 100 games. Under which of the following situations would X be a binomial random variable?Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.
- 8Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 35, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?19.25 and 3.437
- 9—The mean daily salary is greater than $350 per day.
Since the mean of X is μx=1(0.05)+2(0.10)+3(0.22)+4(0.30)+5(0.18)+6(0.12)+7(0.03)=3.94, then the mean of Y is μY=a+bμX=150+50(3.94)=$347. Since $347<$350, the statement is false.
- 10Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait. The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?In repeated sampling from the distribution of S , the average of the values will approach 4.66.
The mean of a probability distribution is the long-run average of the values selected from many repetitions. - 11A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?Two
- 12In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 16. What is the probability that it takes three rolls until the player rolls doubles?0.1157
- 13According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 20?0.0463
- 14A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?
- 15In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable B represent the number of people in the sample without the characteristic. Random variable B follows a binomial distribution with a mean of 2.7 people. Which of the following is the best interpretation of the mean?For all groups of 45 people, the average number of people without the characteristic is 2.7.
- 16A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 22 through 29, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?31.0
- 17An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon’s ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram. Based on the results of the simulation, which of the following is closest to the probability that there were at most two successes in a trial?0.79
- 18The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who purchased the extended warranty. Assume customers’ decisions on whether to purchase the extended warranty are independent. Which of the following is closest to the probability that X > 3; that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?1 - gcdf(0.21, 3)
- 19The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R−S ?Mean 3 and standard deviation 5
- 20Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?
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- 10th grade Math Flashcards on Unit 7 - Discrete Distributions Test, created by Kelly Chen on 02/05/2021.
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