Question

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 8.9 pounds and 11.4 pounds, respectively.

a. Calculate the expected value and the standard deviation of this distribution. (Do not round intermediate calculations. Round your "Expected value" to 2 decimal places and "Standard deviation" answer to 4 decimal places.)

b. Find the probability that the weight of a randomly selected bag is no more than 11.3 pounds. (Round your answer to 2 decimal places.)

c. Find the probability that the weight of a randomly selected bag is at least 10.8 pounds. (Round your answer to 4 decimal places.)

Answer 1

Solution :

Given that,

a = 8.9

b = 11.4

a) expected value = (a + b) / 2

expected value = (8.9 + 11.4) / 2

expected value = 10.15

standard deviation =  (b - a) / 12

standard deviation =  (11.4 - 8.9) / 12

standard deviation = 0.7217

b) P(x < c) = (c - a) / (b - a)

P(x < 11.3) = (11.3 - 8.9) / (11.4 - 8.9)

P(x < 11.3) = 0.96

c) P(x c) = (b - c) / (b - a)

P(x 10.8) = (11.4 - 10.8) / (11.4 - 8.9)

P(x 10.8) = 0.2400