An event has total six outcomes with probability P₁=1/2, P2=1/4, P3=1/8, P4=1/16, P5=1/32, and P6=1/32. Find the entropy of the system. Also find the rate of information if these are 18 outcomes per second
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- June is a student taking a statistics course. Unfortunately June is not a diligent student she does not read the textbook before or after class does not do homework and regularly misses class. She intends to rely on log to pass the next quiz. The quiz consists of 10 multiple-choice questions. Each question has five possible answers. Only one of the answers is correct, so the probability of choosing the correct answer is 0.20. June plans to guess the answer to each question independently. Let X be the number of correct answers on June’s quiz. A score (I.e, the number of correct answers) is considered failure if it is less than 6. What is the probability that June fails the quiz?The sum of two positive quantities is equal to 2n. Find the probability that their product is not less than 3/4 times their greatest product.A researcher wants to know how long it takes, on average, for a certain species of bacteria to divide. She watches 15 cells through a microscope and times how long it takes them to divide. She obtains the following data, in hours: 6.3, 7.1, 8.7, 6.1, 7.4, 7.5, 6.4, 7.8, 7.5, 4.4, 6.1, 7.1, 5.9, 5.9, 7.6 Construct a 95% confidence interval for the average time it takes this species of bacteria to divide. S = %D Margine of Error: E = We are 95% confident that this species of bacteria takes, on average, between hours to divide. hours and
- 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 collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to a certain company for a given employee turnover percentage in a year.
- The height ( in inches) of a plant x months after an experiment begins is given byA researcher wants to know how long it takes, on average, for a certain species of bacteria to divide. She watches 17 cells through a microscope and times how long it takes them to divide. She obtains the following data, in hours:6.7, 10.5, 4.8, 5.2, 5.2, 10.6, 4.4, 5.7, 10.9, 7.5, 5.3, 4.4, 5.7, 5.2, 6.9, 4.5, 7.7Assuming the population standard deviation is σ=2σ=2, construct a 94% confidence interval for the average time it takes this species of bacteria to divide.xˉ=x̄=α2=α2=zα2=zα2=Margin of Error: E=E=We are 94% confident that this species of bacteria takes, on average, between hours and hours to divide.___Arbor Systems and Gencore stocks both have a volatility of 44%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is 0.00. If the correlation is 0.00, the volatility of the portfolio is%. (Round to one decimal place.)
- An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure " distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group: Distance xx 2 5 4 4 4 6 Days yy 4 21 29 40 47 49 Use a calculator or software to find the following values. (a) Find the mean and standard deviation of xx. MEAN: STANDARD DEVIATION: (b) Find the mean and standard deviation of yy. MEAN: STANDARD DEVIATION: (c) Find the correlation rr between xx and yy. r:You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a) Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast."Space Mountain", a classic attraction at Disneyland Park, attracts many tourists to take a ride. Each ride can take tourist at a rate of 5 persons/min. The park is opened at 9:00 AM. Based on daily observations, it is found that the tourist arrival rate is 8 persons/min during 9:00 AM - 12:00 PM, 5 persons/min during 12:00 PM - 3:00 PM and 2 persons/min after 3:00 PM. Apply a D/D/1 queuing model to calculate what is the maximum number of tourists waiting in the queue? (Round to the nearest integer and fill in the blank with a number only.) Tourist # 180 D/D/1 360 Time (min) A
