Question

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

Answer 1

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%