The numbers of accidents which occur on an assembly line each week over a2 year period are summarised in Table 1.Table 1:Number of accidents,018695 AWNI234678Frequency1142136189212(a) Use the data to compute the sample mean number of accidents recordedper area.(b) Suppose the data in Table 1 follows a Poisson distribution. Calculate thetheoretical Poisson(\ = 3) probabilities for integers in the range 0 to 9inclusive.(c) Does this Poisson distribution provide a good model for the number ofaccidents in this example (as per Table 1)? Explain why or why not. UseR to produce a graph to help support your answer (produce the R as partof your answer).(d) Use the model in (b) to estimate the probability that less than 2 accidentswere recorded in any randomly chosen week. How does this compare tothe actual data?

From the given information, Number of accidents, x Frequency 0 1 1 14 2 21…

Answered: The numbers of accidents which occur on…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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eat out or in The overall change in the consumer price index is a weighted average of changes in various categories. on november 19, 2011 the boston globe reported the data displayed in figure 5.7. is it reasonable to say that about 40% of food expenses are for food away from home?
Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows. Age of Moose in Years Number Killed by Wolves Calf (0.5 yr)1-56-1011-1516-20 1084870682 (a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.) 0.5 1-5 6-10 11-15 16-20 (b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.) μ = σ =
An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
A report states that 45% of American adults were obese. In this report, adults were considered to be 20 years of age or older. If about 71% of Americans are adults (20 and over), use the U.S. population estimate of 301 million people to calculate the number of American adults age 20 and older.
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 milimeters, and a Variance of 64. If 416 rods are sampled at random from the batch, what is the probability that the mean length all the sample rods would differ from the population mean by less than 0.65 millimeters? Round your answer to four decimal places.
The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm². (a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 4? (Use L=3) (b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? (c) Continue b), what is the probability of detecting this mean shift before plotting the 5th sample after the mean shift?
. A process that cuts lengths of metal with high precision has historically produced metal rods with length that is normally distributed and with a mean of 800 millimetres (mm). Management at the factory is concerned that after an overhaul of the machine the mean length of the rods being produced could differ from the required 800 mm. If it is found that the rods are not being produced to specifications then the machine will have to be stopped for readjustment, with a consequent loss of production. The production line manager tasked with investigating the issue finds that a (random) sample of 25 rods yielded a mean length of 806 mm and a sample standard deviation of 10 mm. i. The mean of the sample is clearly not the required 800 mm. Say why this is not enough information in itself to say if the machine is operating correctly or not. ii. State the null and alternative hypotheses for this situation.

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