It is known that if bacteria are grown on a maintenance board of area A, and if Y = thenumber of colonies of bacteria in a small area a selected at random from the board,then Y has a Poisson distribution with a mean alA (number of colonies on the entireboard). Suppose p = 5.5,Calculate the probability that:(a) At most 3 colonies were found in that area.(b) More than 8 colonies will be found in the area.

We want to find following probability X~Poisson(μ=5.5)

Answered: It is known that if bacteria are grown…

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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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?
Please note the question is: What is the distribution of the t-test statistic if m, n -----> ∞ ?
Suppose a data set from a bike share company contains the number of daily bike rentals at each of 6 stations for the 23 weekdays of a particular month, i.e. we have Yij for i = 1, ..., 23 and j 1,...6. Write down a hierarchical normal model that can be used to estimate the mean number of bike rentals at each station. You can assume that the unknown variance o? of the number of bike rentals is the same for each station.
4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
Suppose X1,..., Xn is a random sample from an exponential distribution with mean e. If X = 17.9 with n = 50, find (a) a one-sided 95% confidence interval for 0, and (b) a two-sided 95% confidence interval for 0.
Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min². (a) What are the values of a and B? α = B = (b) What is the probability that a student uses the terminal for at most 18 min? (Round your answer to three decimal places.) (c) What is the probability that a student spends between 15 and 27 min using the terminal? (Round your answer to three decimal places.)
Assume that the helium porosity (in percentage) of coal samples taken from anyparticular seam is normally distributed with true population variance 0.36.(a) Compute a 95% two-sided CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. (b) How large a sample size is necessary if the width of the 95% two-sided CI is to be 0.5? (c) Compute a 98% upper one-sided CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.show major intermediate steps.
Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.
Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?
Can you help with part b without using Chebyshev's theorem
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…
5. Daily sales of a store is normally distributed with mean µ=180 Rials and variance o =100. Find the probability that total sales over a period of nine days is more than 1800 Rials. Z= p=

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