Math150
5.4 The probability that a randomly selected individual in a country earns more than $75,000 per year is 7.5%. The probability that a randomly selected individual in the country earns more than $75,000 per year, given that the individual has earned is 21.5%. Are the events "earn more than $75,000 per year" and "earned a bachelor's degree" independent? bachelor's degree, Are these events independent? No
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c). Purchase likelihood 18-34 35-44 45-54 55 + Total More likely 231 306 398 405 1340 Less likely 23 9 20 14 66 Neither more nor less likely 290 208 161 141 800 Total 544 523 579 560 2206
Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(4) = .25 (Type an integer or a decimal.)
In the following probability distribution, the random variable x represents the number of activities a parent of a 6th- to 8th-grade student is involved in. Complete parts (a) through (f) below. to to 1 2 4 P(x) 0.137 0.345 0.133 0.077 0.308 C.
5.5 Find the value of the factorial. 8!
List all the combinations of five objects m, I, n, k, and p taken two at a time. What is C,? List all the combinations of five objects m, I, n, k, and p taken two at a time. Choose the correct answer below.
If a new car has 2 transmission types, 3 vehicle styles, 2 option packages, 7 exterior color choices, and 3 interior color choices, how many different new cars are possible? There are 252 possible different cars.
Once a woman won $1 million in a scratch-off game from a lottery. Some years later, she won $1 million in another scratch-off game. In the first game, she beat odds of 1 in 6.2 million to win. In the second, she beat odds of 1 in 705,600. (a) What is the probability that an individual would win $1 million in both games if they bought one scratch-off ticket from each game? (b) What is the probability that an individual would win $1 million twice in the second scratch-off game?
Will the following variables have positive correlation, negative correlation, or no correlation? IQ and annual salary Will these variables have positive correlation, negative correlation, or no correlation?
Positive
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An investor randomly purchases 12 stocks listed on a stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 45%. The number of stocks that increase in value is recorded. Does the probability experiment represent a biniomial experiment?
A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. n=7, p = 0.55, x<4 The probability of obtaining x successes in n independent trials of a binomial experiment, where the probability of success is p, is given by the following formula. P(x) =,C,p*(1- p)" -×, x=0,1,2,.n
6.1 Determine whether the random variable is discrete or continuous. In each case, possible values of the random variable. (a) The number of fish caught during a fishing tournament. (b) The amount of rain in City B during April. (a) Is the number of fish caught during a fishing tournament discrete or continuous?
Determine whether the distribution is a discrete probability distribution. P(x) D 0.27 0.17 2 0.17 3 0.24 4 0.15 Is the distribution a discrete probability distribution?
5.3 Determine if the following statement is true or false. When two events are disjoint, they are also independent. False
Determine whether the events E and F are independent or dependent. Justify your answer.
A salesperson must travel to eleven cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
A certain three-cylinder combination lock has 70 numbers on it. To open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a three-number lock combination has been effected. Repetitions are allowed, and any of the 70 numbers can be used at each step to form the combination. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try?
How many different simple random samples of size 5 can be obtained from a population whose size is 39? The number of simple random samples which can be obtained is 575757. (Type a whole number.)
A golf-course architect has six linden trees, four white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced? The trees can be planted in 13860 different ways.
Suppose 63 cars start at a car race. In how many ways can the top 3 cars finish the race? The number of different top three finishes possible for this race of 63 cars is 238266. (Use integers for any number in the expression.)
A lottery exists where balls numbered 1 to 18 are placed in an urn. To win, you must match the five balls chosen in the correct order. How many possible outcomes are there for this game? The number of possible outcomes is 1028160 . (Simplify your answer.)
5.2
A probability experiment is conducted in which the sample space of the experiment is S= (7,8,9,10,11,12,13,14,15,16,17,18). Let event E= {8,9,10,11,12,13} and event F = {12,13,14,15). List the outcomes in E and F. Are E and F mutually exclusive? List the outcomes in E and F. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. {12,13 } (Use a comma to separate answers as needed.) D. No. E and F have outcomes in common.
A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. n= 9, p = 0.25, x<4 P(X<4) = 0.8343 (Round to four decimal places as needed.)
According to an almanac, 80% of adult smokers started smoking before turning 18 years old. (a) If 100 adult smokers are randomly selected, how many would we expect to have started smoking before turning 18 years old? (b) Would it be unusual to observe 85 smokers who started smoking before turning 18 years old in a random sample of 100 adult smokers? Why? (a) We would expect about 80 adult smokers to have started smoking before turning 18 years old. (Type a whole number.) (b) Would it be unusual to observe 85 smokers who started smoking before turning 18 years old in a random sample of 100 adult smokers? E. No, because 85 is between u- 20 and u + 20.
5.6 List all the permutations of five objects m, I, n, ,and p taken two at a time without repetition. What is P,? List all the permutations of five objects m, I, n, and p taken two at a time without repetition. Choose the correct answer below. A. ml, mn, mk, mp, Im, In, Ik, Ip, nm, nl, nk, np, km, kl, kn, kp, pm, pl, pn, pk O B. ml, mn, mk, mp, In, Ik, Ip, nk, np, pp O C. m, I, n, k, p O D. mm, ml, mn, mk, mp, II, In, Ik, Ip, nn, nk, np, kk, kp, pp What is P2? 20 (Simplify your answer.)
An essay test has 11 questions. Students are required to answer 9 of the 11 questions. How many different sets of questions could be answered? Does the order matter in the arrangements of this problem?
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Three cards are selected from a standard 52-card deck without replacement. The number of tens selected is recorded. Does the probability experiment represent a binomial experiment?
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. A soccer goalie who stops 37% of her shots is asked to make saves until she gives up a goal. The number of saves attempted is recorded. Does the probability experiment represent a binomial experiment?
4.1 Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. 020400102030ExplanatoryResponse A scatter diagram has a horizontal axis labeled "Explanatory" from 0 to 40 plus in increments of 10 and a vertical axis labeled "Response" from 0 to 30 in increments of 5. The following 18 approximate points are plotted, listed here from left to right: (5, 3); (5, 6); (10, 5); (12, 8); (15, 9); (15, 6); (18, 9); (21, 11); (21, 14); (25, 13); (25, 16); (30, 15); (30, 17); (35, 18); (42, 21); (42, 23); (50, 25); (50, 28). The points generally rise from left to right at a constant rate.
Do the two variables have a linear relationship? The data points have a linear relationship because they lie mainly in a straight line. Do the two variables have a positive or a negative association? B. The two variables have a positive association.
On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.714. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean.
Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below. Yes, since 0.714 is greater than the critical value for 30. What does this result mean? A. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam
What does it mean if r=0?
No linear relationship exists between the variables.
What is the probability of obtaining two heads in a row when flipping a coin? Interpret this probability. The probability of obtaining two heads in a row when flipping a coin is 0.25. (Round to five decimal places as needed.) Interpret this probability. Consider the event of a coin being flipped two times. If that event repeated ten thousand different times, it is expected that the event would result in two heads about 2500 time(s). (Round to the nearest whole number as needed.)
Question Help About 10% of the population of a large country is math phobic. If two people are randomly selected, what is the probability both are math phobic? What is the probability at least one s math phobic? Assume the events are independent. (a) The probability that both will be math phobic is 0.01 (Round to four decimal places as needed.) (b) The probability that at least one person is math phobic is 0.19. (Round to four decimal places as needed.)
Suppose George wins 45% of all chess games. (a) What is the probability that George wins two chess games in a row? (b) What is the probability that George wins five chess games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that George wins five chess games in a row, but does not win six in a row.
Suppose Ari wins 45% of all checker games. (a) What is the probability that Ari wins two checker games in a row? (b) What is the probability that Ari wins six checker games in a row? (c) When events are independent, their complements are independent as well. Use this result six checker games in a row, but does not win seven in a row. determine the probability that Ari wins
Suppose you just received a shipment of ten televisions. Two of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Suppose there is a 26.6% probability that a randomly selected person aged 25 years or older is a jogger. In addition, there is a 10.6% probability that a randomly selected person aged 25 years or older is female, given that he or she jogs. What is the probability that a randomly selected person aged 25 years or older is female and jogs? Would it be unusual to randomly select a person aged 25 years or older who is female and jogs?
The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below. LOADING... Click the icon to view the critical values for the correlation coefficient. Commute Time (in minutes) Well-Being Score 5 69.5 13 68.9 23 67.7 36 67.6 54 66.5 67 65.4 104 63.9
Which variable is likely the explanatory variable and which is the response variable? D. The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score. b) Draw a scatter diagram of the data. Which of the following represents the data? B. 01106070Commute Time (min)Score A scatter diagram has a horizontal axis labeled "Commute Time (minutes)" from 0 to 110 in increments of 10 and a vertical axis labeled "Score" from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (6, 69.6); (14, 69.0); (24, 67.8); (36, 67.6); (54, 66.6); (68, 65.4); (104, 64.0). The points follow the general pattern of a straight line that falls from left to right. (d) Does a linear relation exist between the commute time and well-being index score? A. Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value.
4.4 A survey asks questions about one's happiness and health. One would think that health plays a role in one's happiness. Use the data in the accompanying table to determine whether healthier people tend to also be happier. Treat level of health as the explanatory variable. LOADING... Click the icon to view the data table. Create a conditional distribution for the data. Level of Health Level of Happiness Poor Fair Good Excellent Not too happy 0.3490.349 0.2090.209 0.1030.103 0.0660.066 Pretty happy 0.4780.478 0.5800.580 0.6110.611 0.4710.471 Very happy 0.1730.173 0.2100.210 0.2860.286 0.4630.463 Total 1.0001.000 1.0001.000 1.0001.000 1.0001.000 (Round to three decimal places as needed.) Use the conditional distribution to determine if healthier people tend to be happier. Choose the correct answer below.
Yes; the percent that are not happy decreases when health increases.
Match the linear correlation coefficient to the scatter diagram. The scales on thex- and y-axis are the same for each scatter diagram. (a) r=0.787, (b) r=1, (c) r=0.946
(a) Scatter diagram III. (b) Scatter diagram II. (c) Scatter diagram I.