Find the mean and variance of the r.v. X if it has p.m.f. P(X=1)=0.2 , P(X=2)=0.3 and P(X=3) = 0.5 ?
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A: Given data, Mean = 69 SD = 7
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A: Consider a random variable X that denotes the test scores. Therefore , X~Nμ=1527,σ=315
Q: A standardized exam's scores are normally distributed. In a recent year, the mean test score was…
A: From the provided information,Mean (µ) = 1473Standard deviation (σ) = 315X~N (1473, 315)
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Q: In a large section of a statistics class, the points for the final exam are normally distributed,…
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2. Find the
3. In a large class, on exam 1, the mean and standard deviation of scores were 78 and 20, respectively, for exam 2, the mean and standard dervationwere 72 and 15, respectively. The
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- Suppose that for the past several decades, daily precipitation in Seattle, Washington has had a mean of 2.4 mm and a standard deviation of 11.4 mm. Researchers suspect that in recent years, the mean amount of daily precipitation has changed, so they plan to obtain data for a random sample of 195 days over the past five years and use this data to conduct a one-sample ?z‑test of ?0:?=2.4H0:μ=2.4 mm against ?1:?≠2.4H1:μ≠2.4 mm, where ?μ is the mean daily precipitation for the last five years. Although they realize that rainfall does not follow a normal distribution, they feel safe using a ?z‑test because the sample size is large. The researchers want to know what the power of this test is to reject the null hypothesis at significance level ?=0.05α=0.05 if the actual mean daily precipitation is 2.6 mm or more. Computing power by hand requires two steps. The first step is to use a significance level of 0.05 to determine the values of the sample mean for which they will reject their null…A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1474 and the standard deviation was 319. The test scores of four students selected at random are 1880, 1190, 2210, and 1380. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The Z-score for 1880 is (Round to two decimal places as needed.) The Z-score for 1190 is (Round to two decimal places as needed.) The z-score for 2210 is (Round to two decimal places as needed.) The z-score for 1380 is (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The unusual value(s) is/are (Use a comma to separate answers as needed.) RECH OB. None of the values are unusual.A professor at a local community college noted that the grades of his students were normally distributed with a mean of 84 and a standard deviation of 6. The professor has informed us that 10 percent of his students received A's while only 2.5 percent of his students failed the course and received F's. a. To the nearest tenth, what is the minimum score needed to make an A? b. To the nearest tenth, what is the maximum score among those who received an F? c. If there were 4 students who did not pass the course, how many students took the course?
- In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)In Company X, the personnel department gives two aptitude tests to applicants. One measures verbal ability while the other measures quantitative ability. From many years of experience, the company has found that a person's verbal score Y1 is normally distributed with mean of 50 and standard deviation (stdev) of 10. The quantitative scores Y2 are also normally distributed with mean of 100 and stdev 20. Y1 and Y2 appear to be independent. A composite score, Y, is assigned to each applicant where: Y= 3Y1 + 2Y2.Applicants whose composite scores are below 375 are automatically rejected. What is the probability that a random applicant gets automatically rejected? If six applicants submit resumes, what are the chances that fewer than half will fail the screening test?In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. The lowest score that would qualify a student for an A is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a B is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a C is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a D is nothing. (Round up to the nearest integer as needed.)
- A new Economic / Social Conservatism Scale has scores between 0 and 30 (0 being extreme liberal, 30 being extreme conservative). The mean score is 21 and standard deviation of scores is 5. You want to convert the original scale (call it X) to a new scale (call it Y) that has scores between 0 and 100. What is the correlation of X and Y?Has the number of shoppers who wear masks changed from 2020 to 2021? There are arguments for and against this question. The mean number of masks, u, used by a shopper in Metropolis in 2020 will be compared to the mean number of masks, Hy used by a shopper in Metropolis in 2021. The true values of u, and u, are unknown. It is recognized that the true standard deviations are o, = 19 for the 2020 measurements and o, = 24 for the 2021 measurements. We take a random sample of m = 255 shoppers in 2020 and a random sample of n = 200 shoppers in 2021. The mean number of masks were x= 97 for 2020 and y= 85 for 2021. Assuming independence between the years and assuming masks used by shoppers are normally distributed we would like to estimate x - Hy. What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y? Create a 95% confidence interval for uy - Hy ? ) What is the length of the confidence interval in part c) ? If we let n stay at 200…In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 73 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)
- The 2011 gross sales of all firms in a large city has a mean of $2.5 million and a standard deviation of $0.6 million. Using Chebyshev's theorem, find at least what percentage of firms in this city had 2011 gross sales of $1.2 to $3.8 million: You are going to apply the Z-score for Normal Distribution and the Area of the Curve for this problem: 1. Sample Mean = 2.5 2. Standard Deviation = .6 3. X = 1.2 (X = data point) 4. X = 3.8 1st Step is to find the Z-score associated to X = 1.2 z= X - μ σ z= 1.2 - 2.5 .6 z = -1.3 .6 Z = -2.16 Now you need to find the Z-score associated to X = 3.8 z= X - μ σ z= 3.8 - 2.5 .6 z= 1.3 .6 Z = +2.16 You need to find the area of the curve that covers Z = -2.16 to Z = +2.16 Go to your Normal Distribution Table in this room Break up 2.16 into 2.1 on the vertical and .06 on the vertical........What is at the intersection? The area of the Curve from Z = 0 to Z = +2.16…just the e partIn a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 71and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.