7. Let's make a guess for how long we would have to wait to see all the air atoms in a balloonmove to one side - it is of course possible at least in principle.a) There are about 1022 atoms in a balloon. We found a single atom had a 50% chanceof being on the left, so two atoms had a 50% times 50% chance of both being onthe left, or 25%, so that three had a 12.5% chance of all three being on the left, andso on. If for any single atom there is a 50-50 chance of being on one side or theother, what is the probability that they will all be on the left side? (If you are havingtrouble calculating this you might want to recall that 10log(x)=x and that log(ab)=blog(a).)b) To change this probability into a waiting time, we need to divide it into the time ittypically takes to change from one configuration into any other. A time that makessense is the time it takes a single atom (moving at about the speed of sound, or 300m/sec) to cross the 0.05 meters from one side of the balloon to the other. How longdo we have to wait then to see this event with some reasonable probability? By wayof comparison, the current age of the universe is roughly 1017 s.

Answered: Image /qna-images/answer/37e92e42-5600-4b70-851e-40404971e18f.jpg

Answered: 7. Let's make a guess for how long we…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A car company conducts crash tests of its new airbag system to evaluate its safety. One hundred cars are run into a solid concrete barrier at a speed of 35 miles per hour, and the chest compression of a crash test dummy is measured each time. They hope that the average compression if the test were repeated over and over (which we could think of as the population) would be about 2 inches, corresponding to an injury that would be painful but not fatal. In the hundred tests, the average chest compression in the crash test dummies was 2.1 inches, with an SD of 0.2 inches.(a) State the null and alternative hypotheses in terms of the problem.(b) What kind of box model will we use for this problem? A 0-1 box, or a box with other values on the tickets?(c) State the null and alternative hypotheses in terms of the box model (d) Compute the z test statistic and the p-value, using the sample average as your statistic as you compute z (e) What do you conclude?
not A 1995 study by the School of Public Health reported that 87% of male students who live in a fraterity house are binge drinkers. The figure for fraternity members who are residents of a fraternity house is 71 %, while the figure for men who do not belong to a fraternity is 44 % Suppose that 11% of U.S. male students live in a fraternity house, 15% belong to a fraterity but do not live in a fraterity house, and 74% do not belong to a fraterity a. What is the probability that a randomly selected malp student is a binge drinker? b. If a randomly selected male student is a binge drinker, what is the probability that he lives in a fraterity house? The probability that a randomly selected male student is a binge drinker is 0.5509 (Type an integer or a decimal rounded to two decimal places as needed) CETTE
1. On the basis of her experience with clients, a clinical psychologist thinks that depression may affect sleep. She decides to test this idea. The sleep of nine depressed patients and eight normal controls is monitored for three consecutive nights. The average number of hours slept by each subject during the last two nights is shown in the following table: (Pagano, 2010). If proved significant, compute of the effect size. Hours of Sleep Depressed patients 7.1 Normal controls 8.2 6.8 7.5 6.7 7.3 7.7 7.8 7.5 8.0 6.2 7.4 6.9 7.3 6.5 6.5 7.2
A company manufacturing CDs is working on a new technology. A random sample of 646 Internet users were asked: "As you may know, some CDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with this technology, or would you refuse to buy it even if it was one you would normally buy?" Of these users, 59% responded that they would buy the CD. Complete parts a and b below. a) Create a 99% confidence interval for this percentage. ( 54.008 %, 63.993 %) (Round to three decimal places as needed. Use ascending order.) b) If the company wants to cut the margin of error by two thirds, how many users must they survey? The company must survey a total of (Type a whole number.) users
Sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question - agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have?
Sarah believes that completely cutting caffeine out of a person's diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah's claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 24 22 24 20…
A researcher wants to determine whether adolescents spend more time in a day around friends than adults do. He gathers a sample of n =10 adolescents (aged 12-17) and a sample of n =6 adults (aged 25-32). The researcher finds that the average time spent around friends for adolescents is M1= 3 hours with a SS1 of 44. He also finds that the average time spent around friends for adults is M2= 2 hours with a SS2 of 40. a. Do you use a one- or two-tailed test? What is the critical/cut-off t value with an alpha level of α = .01? b. What is the variance? c. What is the estimated standard error? d. What is the value of the t statistic? e. Do we reject or fail to reject the null hypothesis (α = .01)? Why? f. Calculate and report the variance explained ( r2)
III. At the Olympic level of competition, even the smallest factors can make a difference between winning and losing. Previous research has found that Olympic marksmen shoot much better when they fire between heartbeats rather than during heartbeats (Pelton, 1983). The tiny vibration of a heartbeat appears to be enough to influence accuracy. A student at the University of Texas attempts to replicate the study with a group of collegiate marksmen. A group of collegiate marksmen (n = 6) fire a series of rounds while the student records heartbeats. For each shooter, a score is recorded for shots fired between and during heartbeats. Do the data support the earlier finding? Use alpha = .05. Shooter During Heartbeats Between Heartbeats A 93 98 В 90 94 C 95 96 92 91 E 95 97 F 91 97 State the hypotheses, critical values with df and alpha = .05, use SPSS and attach the SPSS output (which you've pasted into a word document to save the trees!) AND highlight the test-statistic and any other…
Can a person train to become better at holding their breath? An experiment was designed to find out. Twelve volunteers were randomly assigned to 1 of 2 groups. The 6 volunteers assigned to group 1 were given breath-holding exercises to perform for 2 weeks. The other group was not given any information about the experiment. At the end of the 2 weeks, all 12 volunteers were individually tested to determine how long they could hold their breath. Here are the data (in seconds). Group 1: 90, 88, 70, 110, 75, 105 Group 2: 40, 48, 35, 50, 55, 62 The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than volunteers without training. Let ₁ = the true mean amount of time that volunteers who were given training held their breath and ₂ = the true mean amount of time that volunteers without training held their breath. What are the appropriate hypotheses? Ho: U1 - U2 = 0, Ha:…
A researcher takes a sample of 40 introverts and 40 extroverts and asks them to solve problems in either a crowded room or an uncrowded room. The researcher measures the number of problems solved (numbers can range from 0 problems solved to 25 problems solved). Here are the results Crowded Room Uncrowded Room Introverts M = 12 M = 18 Extroverts M = 18 M = 12 Does there appear to be a main effect of room? Does there appear to be a main effect of personality (introversion/extraversion)? Does there appear to be an interaction between room and personality?
You are interested in finding out if kangaroo rats that have been offered food ad lib(unlimited food) for the previous 24 hours store a different amount of food in their pouches than kangaroo rats that have been starved for 24 hours. You take 8 kangaroo rats and starve them for 24 hours, then offer them food and count how many seeds are stored in their pouches in the next hour. You let your rats rest for one week, and repeat the experiment with the same rats, but offer them unlimited food for the 24 hours prior to the experiment. Run the appropriate statistical test. Rat ID # Seeds (starving) 3 Seeds (ad lib) 1 10 26 2 16 23 3 15 16 4 12 17 5 21 29 6 13 21 7 12 32 8 10 18
1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…

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