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ArbitrLikvidat [17]
2 years ago
8

Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard d

eviation is 2 pounds. Assume the variable is approximately normally distributed. If a household is selected at random, find the probability of its generating:
1) Between 27 and 31 pounds per month.

2) More than 30.2 pounds per month.

Please explain!
Mathematics
1 answer:
Annette [7]2 years ago
4 0

a) For x = 27:

z = 27-28/2 = -0.5

For x = 31:

z = 31-38/2 = 1.5

From the normal distribution table, P(27 < x < 31) = P(-0.5 < z < 1.5) = P(z < 1.5) - P(z < -0.5) = 0.9332 - 0.3085 = 62.47%

b)  For x > 30.2:

z = 30.2-28/2 = 1.1

From the normal distribution table, P(x > 30.2) = P(z > 1.1) = 1 - P(z > 1.1) = 1 - 0.8643 = 13.57%

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f'(x) = {tex}2x + 2y dy/dx = 2(3x^{2} + 4y^{2} - x)(6x + 8y dy/dx - 1){/tex}

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