The probability that a student would take at least 20 minutes to complete both the tasks 1 and 2 when the time for each task performed by the students by the use of the software, MODSTAT is normally distributed and the time taken by the students is independent of the others where for the sum X + Y which is normally distributed, the mean is μ = μ X + μ Y and the standard deviation is σ = σ X 2 + σ Y 2 such that X and Y are independent normal random variables.

Question

For each of the following series, determine whether the absolute convergence series test determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let Mi = 4, while if the test determines absolute convergence let Mi 1 : 2: ∞ Σ(−1)"+¹ sin(2n); n=1 Σ n=1 Σ ((−1)”. COS n² 3+2n4 3: (+ 4: 5 : n=1 ∞ n 2+5n3 ПП n² 2 5+2n3 пп n² Σ(+)+ n=1 ∞ n=1 COS 4 2 3+8n3 П ηπ n- (−1)+1 sin (+727) 5 + 2m³ 4 = 8. Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is -0.027 -0.621 -1.794 -1.132 -1.498 -4.355 -2.000 2.716

Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 9.5, Problem 55E

To determine

To calculate: The probability that a student would take at least 20 minutes to complete both the tasks 1 and 2 when the time for each task performed by the students by the use of the software, MODSTAT is normally distributed and the time taken by the students is independent of the others where for the sum X+Y which is normally distributed, the mean is μ=μX+μY and the standard deviation is σ=σX2+σY2 such that X and Y are independent normal random variables.

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For each of the following series, determine whether the absolute convergence series test determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let Mi = 4, while if the test determines absolute convergence let Mi 1 : 2: ∞ Σ(−1)"+¹ sin(2n); n=1 Σ n=1 Σ ((−1)”. COS n² 3+2n4 3: (+ 4: 5 : n=1 ∞ n 2+5n3 ПП n² 2 5+2n3 пп n² Σ(+)+ n=1 ∞ n=1 COS 4 2 3+8n3 П ηπ n- (−1)+1 sin (+727) 5 + 2m³ 4 = 8. Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is -0.027 -0.621 -1.794 -1.132 -1.498 -4.355 -2.000 2.716

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 9.5, Problem 55E

To determine

To calculate: The probability that a student would take at least 20 minutes to complete both the tasks 1 and 2 when the time for each task performed by the students by the use of the software, MODSTAT is normally distributed and the time taken by the students is independent of the others where for the sum X+Y which is normally distributed, the mean is μ=μX+μY and the standard deviation is σ=σX2+σY2 such that X and Y are independent normal random variables.

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 9.5, Problem 55E

To determine

To calculate: The probability that a student would take at least 20 minutes to complete both the tasks 1 and 2 when the time for each task performed by the students by the use of the software, MODSTAT is normally distributed and the time taken by the students is independent of the others where for the sum X+Y which is normally distributed, the mean is μ=μX+μY and the standard deviation is σ=σX2+σY2 such that X and Y are independent normal random variables.

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 9.5, Problem 55E

To determine