Concept explainers
Suppose
a. How many elements are in the array?
b. How many elements are in the subarray
c. If
d. What is the probability that a randomly chosen array element is in the subarray shown below if
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Chapter 9 Solutions
Discrete Mathematics With Applications
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- A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. 65% of the students have never taken a statistics class, 15% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. Round your answers to three decimal places. a. What is the probability that the first groupmate you meet has studied at least two semesters of statistics? b. What is the probability that the first groupmate you meet has studied some statistics? c. What is the probability that neither of your two groupmates has studied any statistics? d. What is the probability that your two groupmates have studied at least one semester of statistics? e. What is the probability that at least one…arrow_forwardIn a certain city, it was found out that there are 100 residents who are employed in the office of the city mayor. They are classified as follows: 48 female employees 46 married employees 34 employees with more than 15 years of service 19 married females 18 married with more than 15 years of service 17 female with more than 15 years of service 8 married female with more than 15 years of service Questions: How many are married female employees with less than 15 years - service? How many are married male with more than 15 year - service? How many are female single employees with more than 15 years of service? How many are married female with more than 15 year – service? How many are male single employees with less than 15-year service?arrow_forwardThe U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare Southwest Airlines flights, 35% are US Airways flights, and 25% are jetBlue flights. a) Deveiop a joint probability table with three rows (airlines) and twoarrow_forward
- If there are nine distinct items 3 at a time, how many permutations will there be?arrow_forwardA fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (jelly beans) for their 9:55 AM snack. Another group gets a high-protein snack (cheese) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. There is no interaction between the type of snack and the time of test μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM =…arrow_forwardFrom time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…arrow_forward
- From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.arrow_forwardConsider a system of two rolled dice, each having six possible states available to it (six different numbers of dots showing upward). According to classical statistics, how many different arrangements are available to this system (a) if the dice are distinguishable, and if the dice are identical. (b) According to classical statistics, in what fraction of the total number of different configurations do the two dice show the same number of dots? (c) What is the true number of distinguishable configurations available to two identical dice? (d) For what fraction of the distinguishable configurations in (a) do the two dice show the same number of dots?arrow_forwardA certain company sends 50% of its overnight mail parcels via express mail service E1. Of theseparcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Supposethat 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sentvia E3. Of those sent via E2 only 2% arrive late, whereas 5% of the parcels handled by E3 arrive late.a. Draw a tree diagram for this problem.b. If a record of an overnight mailing is randomly selected from the company’s file, what is theprobability that the parcel went via E2 and was late?c. What is the probability that a randomly selected parcel arrived on time?d. If a randomly selected parcel has arrived late, what is the probability that is was not sent via E1?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage