In the efforts to reduce road accident in Tanzania, the traffic police have launched a new program, in which drivers who are found with traffic offence three times are given the option of whether to attend a special training program or to pay a fine 200,000 Tanzanian shillings. Suppose that 20% of all drivers in Dar es Salaam were found with traffic offences three times within the past year. Assume that 80% of those found with three traffic offences attended the training program so that they would not have to pay the fine. If a driver from Dar es Salaam is randomly selected, what is the probability that he or she found with three traffic offence and attend the training program?

5) Reynoldsburg surveys Summit HS students. They found 90% of students are tired at 7:10am and 40% of those students who are tired at 7:10am are chronically late to school. What percent of all Summit HS students are both are tired at 7:10am and are chronically late to school?

2. One of the country's most pervasive societal issues appears to be violence against women (VAW). According to the Philippine Statistics Authority's 2017 National Demographic and Health Survey, one in every four Filipino women between the ages of 15 and 49 has been subjected to physical, emotional, or sexual assault by their husband or partner. The approximate number of complaints received per day by the Violence Against Women and Children (VAWC) Desk in Pangasinan during the first quarter of 2020 is shown below. Find the mean, variance, and standard deviation of the distribution. Note: P(X) = : %3D X: P(X) X² - P(X) X f 21 P(X) 3 4 16 a2 = 32 15 8. 16 9 10 10 25 11 29 12 24 Standard Deviation Variance | E(x·P(X))= Mean(u) N = P(X) = 1 Ex² · P(X)= 197

5. As of 2021, the country Swaziland in southern Africa (now officially named as Eswatini) had the highest HIV prevalence in the world. 25.9% of the country's entire population is infected with HIV. The Elisa Test is one of the first and most accurate HIV testing used in recent times. For those who carry the virus, Elisa test is 99.7% accurate. For those who do not have the virus, the test has 92.6% accuracy. If an individual from Eswatini tested positive, what is the probability that he/she carries the virus?

1) Using the data from the American Community Survey (IPUMS), the Pew Research Center reported that 32.1% of 18- to 34-year-olds was living with their parents in their parents' home in 2014. For the first time in recorded history, this was the most common living arrangement for this age group. What percentage of 18- to 34-year-olds is living at home with their parents this year? To answer this question, suppose that this year researchers conduct another survey with a random sample of 1,100 adults in this age group. Suppose that 35% are living at home with their parents. Assuming that the variability in random samples will be the same as in the 2014 study, find the 95% confidence interval for this year and interpretit. a) Verify that the conditions for the use of the normal model are met based on the Pew Research Center study. b) Calculate the standard error based onthe 2014 study. c) Find the 95% confidence interval for this year and represent it as a line segment. d) Interpret your…

2. Based on past records, it is generally believed that on an average, a typical University of Technology and Applied Sciences, Nizwa student spends about 25 hours in the LRC per week. Recently, the library has been shifted to a new location which is further away from the academic block. As a result, the administration feels that students may be spending less time in the library. Accordingly a random sample of 41 students were selected and the average number of hours they spend in the library came out to be 16.78 with a standard deviation of 5.17. Carry out an appropriate test of hypotheses for the above problem to test whether the shifting of the library has adversely impacted the study time in the population of all students. (You may assume that study times/week approximately follow a normal distribution in the population).

5. A large security-system management company with clients in Los Angeles and San Francisco installs and monitors secu- rity systems in houses and on business premises. The system's alarm sounds at the central monitoring location if the system detects a security break-in, smoke, or fire at any of the clients' premises. Tests have indicated that 3 percent of clients have a false alarm, meaning the alarm sounds when there is no incident, and that in approximately 0.5 percent of actual incidences, the system fails to sound an alarm. The records indicate that about 0.1 percent of clients have break-in/fire/smoke incidents. (a) Suppose a client is selected at random. What is the probability that the alarm will sound at this client's premises? (b) Suppose the alarm is sounded at a client's premises. What is the probability that there is no break-in, smoke, or fire inci- dent? ELE

5. According to the Ameriprise Financial Money Across Generations study, 9 out of 10 parents with adult children ages 20 to 35 have helped their adult children with some type of financial assistance ranging from college, a car, rent, utilities, credit card debt, and/or down payments for houses. The following table with sample data consistent with the study 21Page shows the number of times parents have given their adult children financial assistance to buy a car and to pay rent. Pay Rent Yes No Buy a car Yes 583 529 No 169 788 a. Develop a joint probability table and use it to answer the remaining questions. If parents did not provide financial assistance to buy a car. what it the probability that the parents assisted with paying rent? cIs financial assistance to buy a car independent of financial assistance to pay rent? Use probabilities to justify your answer. b.

A survey conducted five years ago by the health centre at a university showed that 18% of thestudents smoked at the time. This year a new survey was conducted on a random sample of 200students from this university, and it was found that 40 of them smoke. a) State the population proportion. b) Determine the sample proportion for students who did not smoke. c) Do these data provide convincing evidence to suggest that the percentage of students whosmoke has changed over the last five years?

1.   A local government official observes an increase in the number of individuals with cardiovascular and obesity problems in his barangay. In order to improve the health conditions of his constituents, he aims to promote an easy and cheap way to reduce weight. It is known that obesity results in risk of having illnesses like diabetes and heart problems. He encouraged his constituents to participate in his Dance for Life project every weekend for three months. To know if the program is effective in reducing weight, he randomly selected 12 participants from the group who completed the program. The weight loss data, in kilograms, of the 12 randomly selected participants after completing the program, are 0.5, 0.7, 0.9, 1.1, 1.2, 1.3, 1.4, 2.0, 2.3, 2.4, 2.7, and 3.0. It is known that the weight loss of those who have completed the dance program follows a normal distribution with variance of 3.24 kg2.   a. Construct and interpret a 90% confidence interval for the true mean weight loss of…