A standard 6-sided die is a cube, which is one of the five platonic 3-dimensional solids. The icosahedron is a 3-dimensional shape with 20 triangular sides, and is used as dice in some games (e.g., Dungeons and Dragons) to allow more variable random outcomes. Over the course of a game, a player records the outcome of several die rolls: 19 7 15 20 4 1 8 18 1 3 3 4 14 10 7 1 4 8 1
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- 1. A researcher observed a rat respond for a food reward by pressing one of the three levers in a cage. Pressing the lever to the right (R) produced no food reward. pressing the lever to the left (L) produced a single food pellet, and pressing the lever at the center (C) produced two food pellets. Because the center level produced the largest reward, the researcher hypothesized that the rat would press this lever most often. Each trial ended when the rat produced a level. The researcher recorded lever pressing for 30 trials. L, L, R, L, R, C, R, L, C, L, L, C, C, C, R, C, R, C, L, C, C, L, C, C, C, L, C, C, C, C, C - Create the appropiate graph for this data - Do these data support the hypothesis? Explain. 2. Which scales of measurement are assumed to be discrete? What does this mean? Which scales of measurement are assumed to be continuous? What does this mean? 3. What type of graph should you create to visualize the following frequency data? Explain. -…A prize wheel at a carnival consists of five equal sectors of these colors: red, blue, green, yellow, and orange. If the wheel lands on yellow, the player wins a prize. After observing several spins, a customer suspects that the wheel is not fair. To substantiate this belief, the customer observes 100 consecutive spins of the prize wheel. What are the appropriate hypotheses? H0: The wheel is not fair.Ha: The wheel is fair. H0: The wheel is fair.Ha: The wheel is not fair. H0: The wheel will land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times.Ha: The wheel will not land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times. H0: The wheel will not land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times.Ha: The wheel will land on red 20 times, blue 20 times, green 20 times, yellow 20 times, and orange 20 times.Question content area top Part 1 For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.19 probability of failure. Complete parts (a) through (c) below. Question content area bottom Part 1 (a) Would it be unusual to observe one component fail? Two components? It ▼ would would not be unusual to observe one component fail, since the probability that one component fails, enter your response here, is ▼ greater less than 0.05. It ▼ would would not be unusual to observe two components fail, since the probability that two components fail, enter your response here, is ▼ greater less than 0.05.
- A gardener is interested in seeing if sunlight and fertilizer type interact so that the effect of fertilizer type depends on the amount of sunlight that plants receive. The gardener randomly assigns half of the plants to be in sunlight and half the plants to be in shade. The gardener also randomly assigns half of the plants to receive the new fertilizer and half to receive an old fertilizer. After a month, the gardener measures plant height. 1 What hypothesis test would be most appropriate for answering this research question and why? 2 What are the independent and dependent variables (if any)? 3 How many levels do the independent variable(s) have?Chapter 7, Section 2, Exercise 034 Find the expected count and the contribution to the chi-square statistic for the (Group 2, No) cell in the two-way table below. Yes No Group 1 737 254 Group 2 1162 328 Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.Expected count=contribution to the chi-square statistic=CONDITIONAL AND MARGINAL PROBABILITY - Statistics and probability } 1) In a plant, complex components are assembled on two different assembly lines, A and B. Line A uses older equipment than B, so it is a bit slower and less reliable. Suppose that on a given day line A assembles 8 components, of which 2 have been identified as defective (D) and 6 as non-defective (ND), while B has produced 1 defective and 9 non-defective components. . a) What is the probability that, when selecting a component at random, a defective one will come out? b) If the selected component is defective, what is the probability that it has left line A? What is the probability that it came out of line B?
- Stereograms Stereograms appear to be composedentirely of random dots. However, they contain separateimages that a viewer can “fuse” into a three-dimensional(3D) image by staring at the dots while defocusing theeyes. An experiment was performed to determine whetherknowledge of the embedded image affected the timerequired for subjects to fuse the images. One group ofsubjects (group NV) received no information or justverbal information about the shape of the embeddedobject. A second group (group VV) received both verbal information and visual information (specifically, a draw-ing of the object). The experimenters measured how many seconds it took for the subject to report that he orshe saw the 3D image.a) What two variables are discussed in this description?b) For each variable, is it quantitative or categorical? Ifquantitative, what are the units?c) The boxplots compare the fusion times for the twotreatment groups. Write a few sentences comparingthese distributions. What does the…Child-Proof Bottles. Designing medication packaging that resists opening by children, but yields readily to adults, presents numerous challenges. In the article “Painful Design” (American Scientist, Vol. 93, No. 2, pp. 113–118), H. Petroski examined the packaging used for Aleve, a brand of pain reliever. Three new container designs were given to a panel of children aged 42 months to 51 months. For each design, the children were handed the bottle, shown how to open it, and then left alone with it. If more than 20% of the children succeeded in opening the bottle on their own within 10 minutes, even if by using their teeth, the bottle failed to qualify as child resistant. Identify the a. experimental units. b. response variable. c. factor(s). d. levels of each factor. e. treatments.Suppose two forces Red and Blue, with Red having a starting force = 2, and Blue having a starting force = 1. Engage in a stochastic Lanchester battle assuming square law, in a fight-to-the-finish, with Red a = 0.01 casualties per minute, and Blue b = 0.03 casualties per minute. (a) What is the expected time of the first casualty?(b) What is the probability that there are no casualties in the first 20 minutes?(c) What is the expected number of Red survivors and the expected length of the battle?