An article suggests the uniform distribution on the interval (6.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.(a) What are the mean and variance of depth? (Round your variance to two decimal places.)meanvariance(b) What is the cdf of depth?F(x) =01X < 6.56.5 ≤ x < 1919 ≤ x(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)What is the probability that the observed depth is within 2 standard deviations of the mean value?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.2, and continuing through 590.7. Determine the mean and variance of the lengths. (a) mean Round your answer to two decimal places (e.g. 98.76). (b) variance Round your answer to three decimal places (e.g. 98.765). (b) i
Growth of bacteria culture after one week, represented by its size, is known to follow lognormal distribution with mean of 2 and variance of 0.2. What is the upper and lower quartile of the size of the culture after one week?
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ₁): n = 15, x=0.45, s=1.02 Reduction in Pain Level After Sham Treatment (2): n = 15, x=0.38, s=1.55 a. Use a 0.01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? OA. Ho H1 H2 oc Hoi HH2 H₁: H1 H2 B. Ho: H1 H2 H₁₁₂ OD. Ho H1 H2 The test statistic, t, is (Round to two decimal places as needed.)
H0 : =150.00 kPa H1 :>150.00 kPa b) α= 0.01; sample variance : 1300 freq. table sample deviation : 36.0555 freq. table
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=29, x=0.58, s=0.95 Reduction in Pain Level After Sham Treatment (μ2): n=29, x=0.48, s=1.56 Question content area bottom Part 1 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). What are the null and alternative hypotheses? A. H0: μ1≠μ2 H1: μ1<μ2 B. H0: μ1<μ2 H1:…
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The average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.
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Paramesan cheese is aged for an average of 24 months to allow it to develop the desire richness in flavor the standard deviation for the length of time Parmesan cheese is aged is 3.7 months How long would Parmesan cheese have to be aged in order to be in the 90th percentile? Assume that the data is normally distributed
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (μ1): n=27, x=0.46, s=0.89 Reduction in Pain Level After Sham Treatment (μ2): n=27, x=0.42, s= 1.43 * Find the t stat * Find the p value * state the conclusion * Does the confidence interval support the conclusion of the test * Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? * Is it valid to argue that magnets might appear to be…

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An article suggests the uniform distribution on the interval (6.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? x < 6.5