In England, the most serious emergency calls requesting an ambulance are classified as 'Red 1'. According to data from NHS England, in March 2017, the London Ambulance Service (LAS) received a total of 1597 Red 1 emergency calls. Based on this number and adjusting for variations during the day, suppose that Red 1 calls arriving at the LAS in daylight hours may be modelled as a Poisson process with rate 3 per hour. (iL (2) Calculate and report the probability that three Red 1 calls arrive at the LAS in 30 minutes during daylight hours. (ii) (1) Write down the distribution of the waiting time (in hours) between the arrivals of two successive Red 1 calls at the LAS during daylight hours, including the values of any parameters. (2) Calculate and report the probability that the gap between the arrivals of two successive Red 1 calls at the LAS during daylight hours will exceed 20 minutes.

were Classified 2. Pg, 36-7, 1.4.33. At the beginning of a Study individuals, 3% were Classified as heavy Smokers, 25.1. Smokers, and 72% were classified as as light In the 5 year study, it was determined. that the death rates of the heavy and light Smokers were 6 and 3 times that of non smokers. non- of Smokers, respectively. A randomly selected Participant died over the Syear period: Calculate the probability that the participant а nonsmorcer? was

A study indicates that CB radio use speeds up activity in the brain. As part of a randomized crossover study, 36 participants were ntted with a CB radio device on each ear and then underwent two positron emission topography, or PET, scans to measure brain glucose metabolism. During one scan, the CB radios were both turned off. During the other scan an automated 40- minute muted signal was sent to the radio on the right ear. The order of when the signal was received (for the first or second scan) was randomized. Comparison of the PET scans showed a minor increase in activity in the part of the brain closest to the antenna during the transmission of the automated signal. Was this an observational study or an experiment? Explain why. O The study is an observational study because the researchers cannot control the response variable during the signal. O The study is an observational study because the researchers only observe values of the response and explanatory variables. O The study is…

In a Denver community, 50 cases of diabetes were reported among 15-19 years old out of a total population of 46,000 between September 1 to December 31, 2016. Ten percent (4,600) of the population were between 15-19 years old on April 1, 2016 and the size and age distribution of the population has remained constant. An investigation of the cases in the 15-19-year age group revealed that 22 of the reported cases were contracted prior to September 1. In addition, another 18 cases developed in April and May but were clinically resolved before September 1. What was the cumulative incidence rate of disease in 15-19 year olds per 1,000 population in this Denver community during the period September 1 to December 31, 2016?

The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B.  a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals). b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals). c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).

Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.