1. The shelf life, in days, for bottles of a certain prescribed medicine is a randomvariable having the density function.20,000x > 0,f(x) = { (z+100)3 »elsewhere.Find the probability that a bottle of this medicine will have a shell life of(a) at least 200 days;(b) anywhere from 80 to 120 days.

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Answered: 1. The shelf life, in days, for bottles…

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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8. The lifetime (measured in terms of number of holes drilled in a titanium plate of specified thickness before breakage) of a machining drill bit has a log-normal distribution with parameters µ = 4.5 and o? = 0.64. a) What is the probability that the lifetime exceeds 100 holes. b) What is the median lifetime?
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Let Z be a st andard normal variable. Let mean and standard derviation > 0 be two real numbers. Then, the distribution of the random variableIs X=emean+standard derviation*Z called the Lognorma (mean,standard derviation) distribution. Write a function to generate random variables from this Lognormal distribution using a transformation method and generate a random sample of size n = 1000. Compare the histogram with the lognormal density curve given by dlnorm function in R.
The probability density function of the time you arrive at a terminal (in minutes after 8:00 a.m.) is f(x)=(e^(-x/13))/13 for 0 < x. Determine the following probabilities.Round the answers to 3 decimal places (e.g. 98.765). a) You arrive by 9:00 A.M. b) You arrive between 8:15 A.M. and 8:30 A.M. c) You arrive before 8:10 A.M. on two or more days of five days. Assume that your arrival times on different days are independent.
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A company that makes rice cookers performed some quality control experiments, and found that the number of years before their products would fail has the following probability density function, as described in Desmos demonstration below. Untitled Graph 10 Probability density function 5- 3 00} 4 k=2 10 Show P(X < k) -5 11 powered by What is the probability that a random rice cooker produced by the company would fail between 4.4 and 6.2 years of usage? (Your answer should be a decimal. Round to 4 decimal places if necessary.)
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