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. (a) A continuous random variable X can assume values between X = 2 and X = 8 inclusively. The probability density function is given by a(x + 3), where a is a constant, calculate a and find, P(3 ≤ x ≤ 5). Approximate your answers to 3dp.

. (a) A continuous random variable X can assume values between X = 2 and X = 8 inclusively. The probability density function is given by a(x + 3), where a is a constant, calculate a and find, P(3 ≤ x ≤ 5). Approximate your answers to 3dp.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 7CR
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2. (a) A continuous random variable X can assume values between X = 2 and X = 8 inclusively. The probability density function is given by a(x + 3), where a is a constant, calculate a and find, P(3 ≤ x ≤ 5). Approximate your answers to 3dp. (b) The ttest is a parametric test: i) in what circumstances are these types of tests used and what are the advantages and disadvantages of using them? ii) If such a test was carried out and a p-value of 0.015 was obtained, what could the researcher infer about the null hypothesis? (c) A firm is compacting ground for construction of a highway, measurements of compaction values (densities) are taken at 17 random points around the site. The sample mean was found to be 26 and standard deviation to be 11.4. The site manager would like to determine if the true mean density is at least 20, as specified by their contract before allowing work to continue. They have been told that they can assume that the underlying population of densities follow a normal distribution. Carry out an appropriate test at the 5% significance level to assess and comment on these claims (approximate values to 1dp). Is work able to recommence? (e) Consider the following compaction measures of soil, plot the empirical CDF for the data. How can the smoothness of the plot be improved? 41.7 14.6 22.6 6.4 24.4 32.5 12.4 35.9 39.9 10.4 16.8 26.2
Transcribed Image Text:2. (a) A continuous random variable X can assume values between X = 2 and X = 8 inclusively. The probability density function is given by a(x + 3), where a is a constant, calculate a and find, P(3 ≤ x ≤ 5). Approximate your answers to 3dp. (b) The ttest is a parametric test: i) in what circumstances are these types of tests used and what are the advantages and disadvantages of using them? ii) If such a test was carried out and a p-value of 0.015 was obtained, what could the researcher infer about the null hypothesis? (c) A firm is compacting ground for construction of a highway, measurements of compaction values (densities) are taken at 17 random points around the site. The sample mean was found to be 26 and standard deviation to be 11.4. The site manager would like to determine if the true mean density is at least 20, as specified by their contract before allowing work to continue. They have been told that they can assume that the underlying population of densities follow a normal distribution. Carry out an appropriate test at the 5% significance level to assess and comment on these claims (approximate values to 1dp). Is work able to recommence? (e) Consider the following compaction measures of soil, plot the empirical CDF for the data. How can the smoothness of the plot be improved? 41.7 14.6 22.6 6.4 24.4 32.5 12.4 35.9 39.9 10.4 16.8 26.2
(f) A 99% confidence interval was calculated for heavy metal concentrations measured in µg g-1, in the 17 samples gathered from site 1, [174.60 402.50], however, the principal investigator requires a confidence interval with a length of just L0 = 200 how much additional sampling at the site must he request before construction begins (the sample standard deviation is 161.1)?
Transcribed Image Text:(f) A 99% confidence interval was calculated for heavy metal concentrations measured in µg g-1, in the 17 samples gathered from site 1, [174.60 402.50], however, the principal investigator requires a confidence interval with a length of just L0 = 200 how much additional sampling at the site must he request before construction begins (the sample standard deviation is 161.1)?
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