Apaper roll factory investigates the quality of products. The technicians have confirmed the number ofbrownish spots on each paper roll, X, has the following probability distribution:a)b)XP(X=x)<4040.250.460.370.1>70Find the mean u and the variance o of X.The technicians randomly pick 36 paper rolls from the production line. The average number ofspots on each paper roll in the sample of 36 is denoted by X. Find the mean µ and the varianceo of X.c) Find the probability that X is less than 5.5.

The probability distribution for the number of brownish spots on each paper roll is given.

Answered: A paper roll factory investigates the…

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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4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)
The aim of a study is to test the ratio of variances in the weight of two groups of rats being under a certain drugs A ( group 1) and B ( group 2) . A random sample of 16 rats was selected from group land 13 rats from group 2, Then their weight were recorded. The results are shown in the following table n Mean Median sd group 1 16 3.5 3.0 1.05 group 2 13 2.20 2.0 1.15 F15,12,0.05 =0.404 F19,16,0.025 = 0.386| F16,10,0.025 =0.335 F16,10,0.05 =0.401| F15,12,0.1 = 0.496 | F19,16,0.05 =0.451 F10,16,0.025 =0.286 F12,15,0.05 =0.382 F16,19,0.025 =0.371 F10,16,0.05 =0.354 F12,15,0.1=0.475 F16,19,0.05 = 0.437 Construct a 95% confidence interval for the ratio of the variances. [ Hint: because of the rounding select the closest interval ] O a. None of these O b. [ 2.488, 0.238 ] O c. [ 2.160 , 0.309 ] O d. [2.063 , 0.318]
6.36. Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in 1 week is given by the following table: 1 2 3 4 7 8 p(z) 0.05 0.10 0.12 0.30 0.30 0.11 0.01 0.01 a. Find the mean value of æ (the mean number of systems sold). b. Find the variance and standard deviation of æ. How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its mean value? d. What is the probability that the number of systems sold is more than 2 standard deviations from the mean?
The aim of a study is to test the ratio of variances in the weight of two groups of rats being under a certain drugs A ( group 1) and B ( group 2) . A random sample of 16 rats was selected from group land 13 rats from group 2, Then their weight were recorded. The results are shown in the following table n Mean Median sd group 1 16 3.5 3.0 1.05 group 2 13 2.20 2.0 1.15 F15,12,0.05 = 0.404 F 19,16,0.025 = 0.386 F16,10,0.025 =0.335| F16,10,0.05 =0.401 F15,12,0.1 =0.496 F19,16,0.05 =0.451 F10,16,0.025 = 0.286 F 12,15,0.05 =0.382 F16,19,0.025 = 0.371| F10,16,0.05 = 0.354 F12,15,0.1 =0.475 F16,19,0.05 = 0.437| Construct a 95% confidence interval for the ratio of the variances. [ Hint: because of the rounding select the closest interval ] O a. None of these O b. [ 2.488, O0.238 ] O c. [ 2.160 , 0.309] O d. [2.063 , 0.318]
Given n independent policyholders with individual loss random variables X1, X2, ., Xn, such that the expected value of any policyholder's loss is pph and the variance is o. If the insurer is providing these n policyholders with insurance, find the following (the detailed steps are required): 1. The expected value of the insurer's average loss per policy; 2. The variance of the average loss per policy.
Find the variance of x or the number of cups of coffee. (Do not round intermediate steps but round your final answer to 4 decimal places)
Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.
The mean height of 15-year-old boys (in em) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are nomally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys would be higher than the mean height of the sample of girls 18: O 0 9878 O 0.0062 O 0.9938 0 9972 Let E[X(Y-1)] 10, E[X(Y#1)] 20, V(X) Then E(Y) 8. V(Y) 12 and V(X+Y) 30. O 14/5 12/5 2
2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2
Indrilling a vertical wellbore, the spacing between major fractures are recorded. It has been found that this spacing is having a mean of 180o ft and a variance of 3,240,000 ft In the first 2000 ft drilling, there was no present of major fracture in the well. Determine the probability that there is a major fracture at the depth of 2000-3500 ft. Select one: a.0.57 b.o.43 C. O.19 do 82

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