The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute.(a) What is the probability distribution for x, the number of visits per minute?p(x) =(b) What is the probability that the number of visits per minute is less than or equal to 10? (Round your answer to three decimal places.)(c) What is the probability that the number of visits per minute is greater than 15? (Round your answer to three decimal places.)(d) Within what limits does Tchebysheff's Theorem suggest you would expect the number of visits to this website to lie at least 89% of the time? (Round your answer up to the nearest whole number.)0 tovisits

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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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Today, the waves are crashing onto the beach every 4.4 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.4 seconds. Round to 4 decimal places where possible. The probability that the wave will crash onto the beach between 1.2 and 2.1 seconds after the person arrives is P(1.2 < x < 2.1) = The probability that it will take longer than 3.28 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.28) = Suppose that the person has already been standing at the shoreline for 0.7 seconds without a wave crashing in. Find the probability that it will take between 3 and 3.7 seconds for the wave to crash onto the shoreline. 62% of the time a person will wait at least how long before the wave crashes in? seconds. Find the minimum for the upper quartile. seconds. Hint:
The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide
A professor knows that her statistics students' final exam scores have a mean of 80 and a standard deviation of 12.2. In her class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 7 students or more will score an "A" on the final exam?Hint: You will need to use your knowledge of normal probability distributions to determine the probability of one individual getting an A and then use your knowledge of binomial distributions to determine the probability of 7 students or more out of 25 students getting an A.prob = ____________Report your final answer accurate to 4 decimal places. Do not round any of the numbers in this calculation until the very end of the problem!
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Discuss the connection between the Poisson and exponential distributions.
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The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 Xhr
The per capita energy consumption level (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal distribution, as shown in the figure. H=2267 kWh VE o=574.7 kWh 2267 Kilowatt-hours 267 X 4267 (a) What consumption level represents the 6th percentile? (b) What consumption level represents the 17th percentile? (c) What consumption level represents the third quartile?
%23 The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts (a) through (c) below. Number of Accidents P(X= x;) Daily (X) 0.28 0.31 0.17 3 0.09 0.07 0.05 4 0.03 a. Compute the mean number of accidents per day. (Type an integer or a decimal. Do not round.) More data-3_24_2022-4..xlsx 67 F e Type here to seareh
The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr

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