The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type has a Poisson distribution with a mean value of 2 specks per square yard. Consider a random sample of \( n = 5 \) film specimens, each having area 1 square yard, and let \(\bar{X}\) be the resulting sample mean number of dirt specks. Obtain the first 21 probabilities in the \(\bar{X}\) sampling distribution. [Hint: What does a moment generating function argument say about the distribution of \( X_1 + \cdots + X_5 \)?]

Given data The number of dirt specks on a randomly selected type has a poision distribution with a…

Answered: The number of dirt specks on a randomly…

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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Recall that Benford's Law clalms that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The…
Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, B = 1.8, and y = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below, :- le-(x/B)a pa a x 2 0 f(x; а, B) %3D x 1.5). (Round your answer to four decimal places.) 0.8050 (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) 1.878 X days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean days standard deviation days
Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(
Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(
The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.5 feet and a standard deviation of 5.75 feet. Random samples of size 19 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution. The mean of the sampling distribution is u- %3D The standard error of the sampling distribution is o, = X. (Round to two decimal places as needed.) Choose the correct graph of the sampling distribution below. O A. В. OC. 2. 51.9 54.5 57.1 43.0 54.5 66.0
It says that 1.496 is also wrong for the mean in part D
A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct width

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