Question

MAD 2120-002, Summer 2018, Dr. Vasile LAURIC jordan davis & 8/3/18 12:53 PM Quiz: Q13 (9.3, 9.4, 8.4) Submit Qui This : 1 pt 2 of 12 (5 complete) This Quiz: 12 pts possible A box of oatmeal must contain 18 oz. The machine that fills the oatmeal boxes is set so that, on average, a box contains 19.2 oz. The boxes by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is 0.4 0z? Tilled by the machine have weights that can be closely approximated The probability is (Type an integer or decimal rounded to four decimal places as needed.) Enter your answer in the answer box. Activate Wind 12:55 PM 8/3/2018

Answer 1

The proportion of boxes containing less than 18oz is 0.0013

Explanation:

A normal random variable with mean Mu = 19.2 and standard deviation sd = 0.4 is standardized with the transformation:

Z = (X - Mu) / sd = (X - 19.2) / 0.4

For a weight value of 18oz, Z = (18 - 19.2) / 0.4 = -3.00.

P (X <18) = P (Z <-3.00) = 0.0013.

The proportion of boxes containing less than 18oz is 0.0013