Let the random variable X represent the number of purple marbles selected when a group of 4 marbles are selected from 20 marbles, of which 8 are purple, 6 are sky blue, and6 are whiteThe probability mass function X is given below.XexPIX=x)495/484511760/4845a) Find the mean u, or expected value of the variable Xb) Find the variance of and standard devitation a for the random variable X21848/48453672/4845470/4845

It is required to obtain the expected value, variance, and standard deviation of the random variable…

Answered: Let the random variable X represent 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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The number of employed persons in Mexico between 2009 and 2019 can be modeled as a random variable with mean 52269218 employed persons and variance of 7607951381613.1 persons2.The mean of the X-bar sample will be obtained from a random sample of 44 data.What is the probability that X-bar will fall between 51,559,018 and 53,539,565?
9. Carboxy- hemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to have a high percentage of carboxyhemoglobin in their blood (Reference: A Manual of Laboratory and Diagnostic Tests by F. Fischbach). Let x be a random variable rep- resenting percentage of carboxyhemoglobin in the blood. For a person who is a regular heavy smoker, x has a distribution that is approximately normal. A random sample of n-12 blood tests given to a heavy smoker gave the following results (percentage of carboxyhemoglobin in the blood): 9.1 9.5 10.2 9.8 11.3 12.2 11.6 10.3 8.9 9.7 13.4 9.9 Where = 10.49 and s = 1.36. A long-term population mean u -10% is considered a health risk. However, a long- term population mean above 10% is considered a clinical alert that the person may be asymptomatic. We will investigate the claim: the data indicate that the population mean percentage is higher than 10% for this patient? Use a = 0.05. a. Find the test statistic. b. Find the critical…
only need d,e,f
According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 48 minutes and a standard deviation of 5.8 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient and let X be the average time between taking a pain reliever and getting relief for a random sample of size 43. 1. Describe the probability distribution of X and state its parameters u and o: X- Select an answer and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 53 minutes. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem Select an answer to describe the probability distribution of X and state its parameters uz and oy: (Round the answers to 1 decimal place) X - Select an answer v (µx ,ox = and find the probability that the average time between taking a pain reliever and getting…
The fracture strength of bi-tempered glass averages 14.03 (measured in thousands of pounds per square inch) and has standard deviation 2. Suppose we randomly select 100 pieces of bi-tempered glass. Let M be the random variable representing the mean fracture strength of the 100 selected pieces. Let T be the random variable representing the sum of the fracture strengths of the 100 selected pieces. Using R and write the code outa) What theorem will let us treat T and M as approximately normal random variables? Monte Carlo TheoremLaw of Large Numbers 301 TheoremCentral Limit TheoremChebychev's TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 1400? e) What is the 98th percentile of the approximate distribution of T? f) What is the standard deviation of M? g) What is the approximate probability M is greater than 13.99? h) What is the variance of 93M?
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The weights of beagles (dogs) have approximately a normal distribution with u = 17.1 pounds and a standard deviation of o = 1.8 pounds. Suppose that we randomly select n = 64 beagles and measure their weights in pounds. Let X be the random variable representing the mean weight of the selected beagles. Let Xtot be the random variable representing the total weight of the selected beagles. a) About what proportion of beagles have weights between 17 and 18 pounds? b) About what proportion of beagles have weights greater 20 pounds? c) About how many of the 64 sampled beagles have weights less than 16.5 pounds? (nearest integer) d) About how many of the sampled beagles have weights between 17 and 18 pounds? (nearest integer) e) What is the standard deviation of the distribution of X? f) What is the standard deviation of the distribution of Xtot? g) What is the probability that 17 1100? f) Copy your R script for the above into the text box here.
Weights of Lamb after eight weeks after born are normally distributed with mean µ = 14 kg and variance σ 2 = 4. a)Find the probability p that a single lamb has weight less than 12 kg. b) Find the probability that exactly 3 of the next 5 lambs examined will have weights less than 12 kg.
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Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO
Total blood volume (in mi) per body wight (in ke) is important in medical research. For healthy aduks, the red blood cell volume mean is about p = 28 ml/kg.t Red blood cell vokume that is too lom ar too high can indicate a medical problem. Suppose that koger has had seven blood tests, and the red blood cell volumes weré as follows Let x be a random variable that represents Roger's red blood cll volume. Assume that x has a narmal distributian and - 4.75. Do the data indicate that koger's red blood cell valume is different (either way) from a- 28 mi/kg? Use a 0.01 lervel of significance. a What is the leval of sigaicance State the null and alternate hypotheses. Will you use a left-lailed, right-laded, or two-tailed test? O H: - 28 ml/kg; H: 2s m/kg; Ima-tailed o Ho: - 28 ml/ka; H 28 m/ka, let-tailed O Ho: 28 mil/kg: H1:- 28 ml/kg; tmo-tailed O Ho: 28 m/ka, H > 28 m/kg; right-laiked (b) What sampling distribution wil you use? Explain the rationale for your choice of sampling distributian.…

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