cumulative distribution function for heights (in meters) of trees in a forest is F(x).(a) Explain in terms of trees the meaning of the statement F (7) = 0.5.F (7) = 0.5 tells us that i(b) Which is greater, F (7) or F (6)? Justify your answer in terms of trees.because every tree of heighteTextbook and Media% of the trees in the forest haveSame for stormeters also has heightmete

The cumulative distribution function essentially explains the probability a random variable X (say)…

Answered: The cumulative distribution function…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 4ECP

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Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
b) Explain how X can be related to the exponential distribution by using a moment generating function argument.
Vehicle breakdowns are equally likely to occur at any point on a 10 kilometer stretch of a given expressway. An emergency recovery truck is stationed at one end of this stretch of expressway. Assume that the recovery truck travels at a constant speed of 50 kilometers/hour. What is the expected (average) time taken for the recovery truck to reach a vehicle that breaks down on this stretch of expressway?
Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(-λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s). Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
Two mechanics are changing oil filters for the arriving customers. The service time has an Exponential distribution with mean 12 minutes for the first mechanic, and mean 3 minutes for the second mechanic. When you arrive to have your oil filter changed, your probability of being served by the faster mechanic is 0.8. (1) Use simulation to generate 10000 service times and estimate the mean service time for yourself. (2) Summarize your data with R code hist(x, probability = TRUE) and mean(x), where x is an array representing your simulated data. Add to the histogram two vertical lines indicating the simulated mean and the theoretical mean. A histogram can be made based on frequencies. A density histogram can also be made. To get a density histogram, the height of each bar is divided by the total number of values, and then by the length of the bar. Such a histogram has a vertical scale comparable with the probability density function of the distribution from which data are randomly…
Patients arrive at a medical cabinet according to a Poisson distribution at rate of 6 patients per hour. The waiting room does not accommodate more than 4 patients. Examination time per patient is exponential with mean 15 min and is done by one doctor. Find the effective arrival rate at the clinic.
Battery life between charges for the Motorola Droid Razr Maxx is 25 hours when the primary use is talk time. The battery life drops to 12 hours when the phone is primarily used for Internet applications over cellular. Assume that the battery life in both cases follows an exponential distribution. a) What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last no more than 15 hours when its primary use is talk time? Compute four decimal places b) What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 20 hours when its primary use is talk time? Compute four decimal places c) What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 5 hours when its primary use is Internet application? Compute four decimal places
The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that: (a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean m for all bulbs of this type. (b) the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution. (c) the average burnout time of a large number of bulbs has a sampling distribution with a similar shape not not as extreme (skewed not not strongly) as the population distribution. d. the average burnout time of a large number of bulbds has the sampling distrbution that is close to normal. d. the average burnout time of a large number of bulbds has the sampling distrbution that is exactly normal.
The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)
In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square test for the lower-side by using the formula and not the excel please)
"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x) = k x10 x > 1 0 x ≤ 1 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)

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