At a border inspection station, vehicles arrive at a rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion. What is the average length of the waiting line? Note: Round your answer to 2 decimal places.   What is the average total time it takes for a vehicle to get through the system? Note: Round your answer to the nearest whole number.   What is the utilization of the inspector? Note: Round your answer to 1 decimal place.   What is the probability that when you arrive there will be three or more vehicles ahead of you? Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.

Suppose that we want to determine if the average amount of timespent online by the students is lessthan 4.5 hours/day. To this end, weconduct a survey of students and askthem how long they spend online perday. We obtain the following results:4.1, 4.3, 4.3, 4.5, 4.6, 4.3, 4.1, 4.6,4.7, 4.6, 4.7, 4.1, 4.3, 4.3, 4.5, 4.6,4.3, 4.1, 4.6, 4.7, 4.6, 4.7, 4.5, 4.6,4.3, 4.1 Assume that the number ofhours spent online has a normal distribution. Test your hypot

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A survey found that in a sample of 100 families, 37 owned cats. A survey done 5 years ago found that in a sample of 80 families, 34 owned cats. At ? = 0.05 has the proportion of cat owners changed over the 5-year period?

A political newspaper, Politically Sound, is interested in the distances voters in Rising Falls County live from their nearest polling station. Politically Sound has hired you to estimate the population mean of all such distances for voters in this county. To estimate this population mean, you select a random sample of 17 Rising Falls County voters and record the distance (in km) each voter lives from their nearest polling station. Assume the population is approximately normally distributed. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of all the distances voters in Rising Falls County live from their nearest polling station. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results for your random sample. Take Sample Number of voters 17 Sample mean 4.757 Sample standard deviation 2.363 Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the…

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Use the t3 I calculator.

A sample of students is to be selected to estimate the proportion who have recieved a medical examination during the past year.  The survey found that x =567 students were examined during the past year.  Construct a 95% interval estimate of the population proportion if the sample size was n=700

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:

A researcher designed a study to test whether caffeine use enhanced performance time to run a 100 meter sprint. The participants (n=30) ran a 100 meter sprint before the consumption of caffeine on day 1 and then they ran another 100 meter sprint on the following day 2 after ingesting caffeine. The average time taken to run the 100 meter sprint on day 1 was (M1) and the average to run on day 2 after caffeine was (M2). The variance for this study was calculated to be (S2).  Does caffeine use improve the running time in the 100 meter sprint (e.g., lower time)?  Use all of the data provided to you below and test at an alpha of 0.05. M1 = 26.53M2 = 14.69S2 = 207.75n=30 a) state null and alternate hypothesis b) what is the critical value  c) what is the obtained value  d) conclusion