2. A certain factory produces X, specialized parts on day n, where X, areindependent and identically distributed random variables with mean 6and variance 9. Let S„be the total number of specialized parts producedfrom day one to day n. Using Central Limit Theorem, determine the totalnumber of parts, a, the said factory can guarantee to produce by day 50with at least 99.9% certainty, i.e., determine the maximum value of a sothat P(S50 2 a) > 0.9999. Note that this maximum value must be awhole number

Central Limit Theorem: When sampling represents the normal distribution and the size of the sample…

Answered: 2. A certain factory produces X,…

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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Estimate the indicated probabny by using the normal distribution as an approximation to the binomial distribution. 6) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.
6. If $X_{1}, X_{2}, X_{3}$, and $X_{4}$ are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, compute the correlations of (a) $X_{1}+X_{2}$ and $-X_{2}+X_{3}$. (b) $X_{1}+X_{2}+X_{3}$ and $X_{3}+X_{4}$. CS. JG. 083
Each passenger on a plane brings one piece of luggage. The weight of a piece of luggage is normally distributed with mean 50 pounds and variance 150 pounds^2. The weight is independent across passengers. The total luggage weight on the plane cannot exceed 1000 pounds. What is the maximum number of passengers allowed such that with at least 0.9 probability the luggage weight is below the limit.
The grade scored by Mehmet in a course is normally distributed with a mean of 50 and standarddeviation of 4.a) If the probability that Mehmet will pass from this course is 0.8413, what is the passing grade? (Notethat to pass from a score, a student should score a grade which is higher than the passing grade.)b) The grade scored by another student from the same course is again normally distributed with a meanof 56 and standard deviation of 3. Find the probability that this student will score higher grade thanMehmet.
Company XYZ know that replacement times for the portable MP3 players it produces are normally distributed with a mean of 3.3 years and a standard deviation of 0.7 years.a) Find the probability that a randomly selected portable MP3 player will have a replacement time less than 1.76 years?b) If the company wants to provide a warranty so that only 2.2% of the portable MP3 players will be replaced before the warranty expires, what is the time length of the warranty?warranty = years
no. 2
Suppose that X¯, Y¯ be the means of 2 samples of sizes n from a normal population with variance σ^2. Determine n so that the probability will be about 0.95 that the two sample means will differ by less than σ.
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standaard deviation of 7 mintuses. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than 15 minutes (b) between 20 and 27 minutes and (c) more than 30 minutes (a) The probability that a randomly selected athlete uses a stairclimber for less than 15 minutes is ( round to four decimal places as needed )

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