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- A group consists of 5 Democrats and 8 Republicans. 7 people are selected to attend a conference.a. In how many ways can 7 people be selected from this group of 13?b. In how many ways can 7 Republicans be selected from the 8 Republicans?c. Find the probability that the selected group will consist of all Republicans.Suppose the number of cars in a household has a binomial distributionwith parameters n = 8, and p = 20 %.Find the probability of a household having:(a) 1 or 5 cars (b) 3 or fewer cars (c) 1 or more cars (d) fewer than 5 cars (e) more than 3 carsAssume the random variablex is normally distributed with mean u= 86 and standard deviation o = 4. Find the indicated probability. P(x<79) P(x<79)%3D P(x<79) =(Round to four decimal places as needed.)
- Assume the random variable x is normally distributed with mean p= 89 and standard deviation o = 5. Find the indicated probability. P(75Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution 4000. Determine the following in parts (a) and (b): with B 2 and 8 = = a P(X > 5000) b P(X> 8000|X > 3000) c Comment on the probabilities in the previous parts compared to the results for an expo- nential distribution.If the random variable X is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(X ≥ .75) is: (a) 0.2266 (b) 0.4525 (c) 0.7734 (d) 0.7500 (e) None of the aboveSuppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.Assume the random variable x is normally distributed with mean µ = 88 and standard deviation o = 4. Find the indicated probability. P(78Let the random variable X denote the length of time (in seconds) required to complete a certain task. Suppose that the completion times are normally distributed with a mean of 216 seconds and a standard deviation of 50 seconds. (i) Find the probability that the time needed to complete the task is between 260 and 290 seconds. (ii) Find the value of k if P(X < k) = 0.025. (iii) A random sample of 25 similar tasks is selected. Find the probability that the mean completion time will be more than 200 seconds.A random variable follows the continuous uniform distribution between 10 and 210. a. Calculate the following probabilities for the distribution. 1. P(75 sxs 85) 2. P(40Assume the random variable x is normally distributed with mean µ = 85 and standard deviation o = 4. Find the indicated probability. P(x<77) P(x<77) = (Round to four decimal places as needed.)Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON