Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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!


Sagot :

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%