Consider a small shop with only one checkout counter. The arrivals of customers are distributed throughoutthe day such that a line rarely forms at the counter. Suppose the arrival times of customers at the counterfollows the Exponential Distribution: XЕap(0.4).0.40.33 0.20.10.00.02.55.07.510.012.515.0a. What is the mean time (in minutes) between customers?b. Determine the following probability.P(2 < X < 10) Suppose X - U(2, 7). Determine P(X > 6 | X > 5).Note: This is a very challenging problem.

Solution Dear student as per guidelines we answer the first question only when multiple questions…

Answered: Consider a small shop with only one…

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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May is tornado season in Oklahoma. According to the National Weather Service, the Poisson rate of tornados in Oklahoma in May is 0.7 per day, based on data from 1950 to the present. The meteorologist is interested in X= the time (in days) from the start of May until the 3rd tornado to occur. Which distribution is an appropriate model for the distribution of X? Gamma Poisson Exponential Beta
Terri Vogel, an amateur motorcycle racer, averages 129.14 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.b. Find the proportion of her laps that are completed between 131.08 and 134.03 seconds. ___________________c. The fastest 2% of laps are under seconds.____________________d. The middle 70% of her laps are from ____ seconds to ____ seconds.
Complete the following table From the frequency distribution, find the mean. Interval Midpoint x Frequency F Product xf 41.5-48.5 11 48.5-55.5 15 55.5-62.5 19 62.5-69.5 25 69.5-76.5 3 76.5-83.5 2
Suppose that replacement times for washing machines are normally distributed with a mean of μ= 8.7 years and a standard deviation of σ= 1.6 years. Find and graph P25 the replacement time that separates the bottom 25% from the top 75%.
A study conducted by Hershey's discovered that Americans consumed an average of 11.4 pounds of chocolate per year. Let's assume that the annual chocolate consumption follows the Normal distribution with mean 11.4 pounds and a standard deviation of 3.6 pounds. Answer the following questions, performing all computations with Excel functions.
Suppose a population is known to be normally distributed with a mean, μ, equal to 144 and a standard deviation, σ, equal to 27. Approximately what percent of the population would be between 90 and 198?
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
The type of battery in Jim's laptop has a lifetime (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime (in years) which follows an exponential distribution with parameter A = 1/4. Find the probability that the lifetime of his laptop battery is less than 2.5 years and that the lifetime of his tablet battery is less than 3.2 years. (Answer as a decimal number, and round to 3 decimal places).
The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)
Which of these graphs show a normal distribution probability?
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?

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