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7. What is the expected value for the example on page 4 that involves a contractor? O $37,800 $22,000 O $26,600 O $21,800

7. What is the expected value for the example on page 4 that involves a contractor? O $37,800 $22,000 O $26,600 O $21,800

MATLAB: An Introduction with Applications
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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7. What is the expected value for the example on page 4 that involves a contractor? O $37,800 $22,000 O $26,600 O $21,800
Transcribed Image Text:7. What is the expected value for the example on page 4 that involves a contractor? O $37,800 $22,000 O $26,600 O $21,800
MORE EXAMPLE: Returning to our randomly selected sample of 5 people, we will compute the mean, variance, and standard deviation of x. x P(x) x P(x) x² P(x) 0 0.03188 0.0000000 0.0000000 1 0.15813 0.1581300 0.1581300 2 0.31374 0.6274799 1.2549598 3 0.31124 0.9337201 2.8011604 0.15438 0.6175201 2.4700803 0.03063 0.1531499 0.7657495 1.00000 2.4900000 7.4500800 4 5 Sum: We see that Ex· P (x) = 2.49 and that Σ x2 · P (x) = 7.45008. Using these values we apply our formulas for the mean, variance, and standard deviation. µ = E(x) = [x · P(x) = 2.49 We can use the last column to calculate the standard deviation. Use the calculation o² = x2 P (x) - μ² = 7.45008 - (2.49)² = 1.24998. So o = √1.24998 = 1.118. Example A contractor is considering a sale that promises a profit of $38,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected profit? (expected profit = weighted mean) a) $26,600 b) $22,000 c) $37,800 d) $21,800 Unusual or Significant Measurements We have learned that a result is considered unusual if it has a probability less than 0.05. We will consider an event to be statistically significant when the corresponding p-value satisfies the inequality. p-value < 0.05 The probabilities which we will use for determining significance will be known as p-values. 4
Transcribed Image Text:MORE EXAMPLE: Returning to our randomly selected sample of 5 people, we will compute the mean, variance, and standard deviation of x. x P(x) x P(x) x² P(x) 0 0.03188 0.0000000 0.0000000 1 0.15813 0.1581300 0.1581300 2 0.31374 0.6274799 1.2549598 3 0.31124 0.9337201 2.8011604 0.15438 0.6175201 2.4700803 0.03063 0.1531499 0.7657495 1.00000 2.4900000 7.4500800 4 5 Sum: We see that Ex· P (x) = 2.49 and that Σ x2 · P (x) = 7.45008. Using these values we apply our formulas for the mean, variance, and standard deviation. µ = E(x) = [x · P(x) = 2.49 We can use the last column to calculate the standard deviation. Use the calculation o² = x2 P (x) - μ² = 7.45008 - (2.49)² = 1.24998. So o = √1.24998 = 1.118. Example A contractor is considering a sale that promises a profit of $38,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected profit? (expected profit = weighted mean) a) $26,600 b) $22,000 c) $37,800 d) $21,800 Unusual or Significant Measurements We have learned that a result is considered unusual if it has a probability less than 0.05. We will consider an event to be statistically significant when the corresponding p-value satisfies the inequality. p-value < 0.05 The probabilities which we will use for determining significance will be known as p-values. 4
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