7)Consider a Poisson random variable with a mean of 100. Graph theprobability mass function of a Poisson random variable with mean 100 over the integersupport points 75 to 125. R uses the command dpois to calculate the Poisson prob-ability mass function; you can use seq in R. to generate the support points, or simplyprovide a range of integers using the operator. Overlay a normal curve with mean100 and standard deviation 10 (You can do this in R using the seq (or operator),dnorm and lines commands).

In probability theory, the Poisson distribution is a discrete probability distribution that…

Answered: 7) Consider a Poisson random variable…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Rods are produced in large quantities in a factory. The masses of these rods are normally distributed with mean 250g and variance 9g. A random sample of 100 rods is selected. Find the probability that the mean mass of the rods in the sample will lie between 249g and 251g. If the rods are produced in batches of n and a batch is selected at random, find the least value of n such that the probability that the mean mass of the rods in the batch will lie between 249g and 251g is greater than 0.95.
In a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…
Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°, 50 water samples will be taken at randomly selected times and the temperature of each sample recorded. The resulting data will be used to test the hypotheses Ho: μ = 150° versus H₂: μ > 150°. In the context of this situation, describe type I error. a A type I error occurs when our estimate for the mean discharge temperature is higher than the actual temperature. A type I error occurs when we say that the plant is not in compliance when in fact it is. A type I error occurs when our estimate for the mean discharge temperature is lower than the actual temperature. A type I error occurs when we…
An elevator has a play card stating that the maximum capacity is 1980 pounds 12 passengers so 12 adult male passages can have a mean way of up to 1180÷12 = 165 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. Assume that weights of males are normally distributed with a mean of 172 pounds and a standard deviation of 27 pounds. Does this elevator appear to be safe?
You studied a third CPU and found that its speed is a continuous random variable that follows a normal distribution, with a mean value of 3.6 GHz and a standard deviation of 0.8 GHz. Find the probability that the third CPU would run faster than the expected speed of CPU1.
Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.4 hours with a standard deviation of 0.3 hours. For a random sample of 6 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.05 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using…
Compute the mean and standard deviation of the time spent for studying andcurrent CGPA for male and female.
Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.f. Why are the estimated waits in this system so long? Are the assumptions behindthem reasonable? Why or why not?
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 7 trials of this experiment. 541, 800, 667, 362, 542, 667, 800 Send data to calculator (a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. 1 2 (b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: 0 O two modes: and ?

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