USN2ENG said:Homework Statement
A machine fills cereal boxes, normally distributed, with standard deviation of .1 oz. What amount setting should the machine be set to if only 1% of the boxes can have less than 16oz of cereal?
Homework Equations
The Attempt at a Solution
I am thinking that I just manipulate the confidence interval for a normal distribution. So x - 2.33(σ) = 16, with 2.33 being the z-score for 99%. My amount would then be 16.233. Am I way off? Thanks
An interval for a normal distribution is a range of values that contains a certain percentage of the data points in a normal distribution. It is often used to estimate the likelihood of a data point falling within a specific range of values.
The interval for a normal distribution is typically calculated using the mean and standard deviation of the data. The interval is defined as the mean plus or minus a certain number of standard deviations. The number of standard deviations used is determined by the desired percentage of data points to be included in the interval.
The interval for a normal distribution is significant because it allows us to make predictions about the likelihood of a data point falling within a certain range. It also provides information about the spread and variability of the data.
No, the interval for a normal distribution is only applicable for data that follows a normal distribution. This means that the data is symmetrically distributed around the mean and follows a bell-shaped curve.
The interval for a normal distribution will change with different confidence levels. A higher confidence level will result in a wider interval, as it includes a larger percentage of the data points. Conversely, a lower confidence level will result in a narrower interval, as it includes a smaller percentage of the data points.