Question

I need help with Standard Deviation!

kellogg's in Kalamazoo, Michigan has a machine that fills the Fruit Loop cereal boxes with cereal. It dispenses cereal with a normal distribution and has a mean of 24.0 and a standard deviation of .1 ounces.

Part A: The middle 95% of cereal boxes contain between ____ and ____ ounces of cereal.

Part B: Approximately 68% of cereal boxes have between ____ and ____ ounces of cereal.

Part C: What percentage of cereal boxes contain more than 24.2 ounces of cereal?

Part D: What is the probability that a randomly selected bottle of cereal contains less than 24.1 ounces of cereal?

Answer 1

A: The middle 95% contain between 23.8 and 24.2 oz.(2 SDs under and over the mean) B: Approximately 68% of boxes have between 23.9 and 24.1 oz of cereal (1 SD under and over the mean) C: 2.5% of boxes contain more than 24.2, because 95% are within 2 SDs, and that includes lower and higher extremes. D: 16% of boxes have more than 24.1, because 68% are within 1 SD of the mean, so 32 are left, and that includes lower and higher extremes.