Find the Value of a Normal Random Variable
-The amount of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 12.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution
A) 12.59 oz
B) 12.09 oz
C) 12.63 oz
D) 12.13 oz

Question

Quizplus · Accepted Answer

To find the 67th percentile of a normal distribution, we can use the Z-score table or a calculator. The 67th percentile corresponds to a Z-score of approximately 0.44. Using the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score, we get X = 12.5 + (0.44)(0.2) = 12.588, which rounds to 12.59 oz.