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Chapter 14 Solutions
Mathematical Methods in the Physical Sciences
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- 3. A box contains 4 black shirts, 8 blue shirts, 4 black pants, and 10 blue pants. Determine the probability of randomly selecting a blue piece of clothing or a pair of pants. Use P(A or B) = P(A) + P(B) = P(A and B) to explain your answer.arrow_forwardIn a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls. (a) Draw a tree diagram showing the possibilities for each outcome. (b) Create the binomial distribution table for P(X). Show all your work.arrow_forwardUnderstanding the difference between independent and dependent events is an important concept of this unit. Post a description of two real-world events-one independent event and one dependent event. Do not state which event is independent and which event is dependent.arrow_forward
- 3. Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,500 skateboards and a standard deviation of 55 skateboards. (a) On what percent of the days last year did the factory produce 20,555 skateboards or fewer? (b) On what percent of the days last year did the factory produce 20,610 skateboards or more? (c) On what percent of the days last year did the factory produce 20,445 skateboards or fewer?arrow_forward2. The table shows the probabilities of winning or losing when the team is playing away or is playing at home. Hom Away Tota e Win 0.2 0.05 0.25 Loss 0.6 0.15 0.75 Tota | 0.8 0.20 1.00 (a) Are the events "winning" and "playing at home" independent? Why or why not? Use probability rules and show calculations to support your answer. (b) Are the events "losing" and "playing away" independent? Why or why not? Use probability rules and show calculations to support your answer.arrow_forwardDecide on a piece of information you want to gather. Select a population and outline a plan on how to determine the sample. You do not need to conduct the actual research. 1. State your population and the piece of information that you want to know. 2. Share your plan for determining the sample.arrow_forward
- 2. Employees were asked how many times per week they exercised. The frequency table shows the results of the survey. Number of times exercised 0 1 N 4 5 6 7 8 Լո per week Frequency 5 10 2 lo 33 12 15 3 1 (a) Create a probability distribution table from the frequency table. Round probabilities to the nearest hundredth. Find: P(x <4) (b) P(x = 6) (c) (d) P(x ≥ 5)arrow_forwardSofie decides to develop a survey. (a) Give an example of a question she could ask on her survey. (b) How could Sofie select a simple random sample of students to take her survey? (c) She gives out 80 surveys but receives only 32 completed surveys. What are the sample and population for Sofie's research? (d) Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. If Sofie uses only the completed surveys, what conclusion could she make about the percent of all high school students who use social media while doing schoolwork?arrow_forward2. The results of a survey show that the percent of adults in a certain town who want to change the name of the town is in the interval [0.38, 0.41] (a) What is the point estimate for the percent who want to change the town's name? (b) What is the poll's margin of error? (c) Do you think the town is most likely to change its name? Which statistic influenced your answer the most? Explain.arrow_forward
- There are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. The first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. The line plot shows the differences after 10 rerandomizations. Determine whether the difference in the means of the two groups is significant based on the line plot. | 0 + 1 XX +2 + 3 XXX 4 5arrow_forward3. The number of visitors to a website in the first week is 50. The number of visitors each week is double the number of visitors the previous week. What is the total number of visitors to the website in the first 8 wk? Show your work.arrow_forward15 Σ (2η – 1) 1. Find the sum of the series n-1 Show your work.arrow_forward
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