Interval for a normal distribution

In summary, the machine should be set to fill the cereal boxes with an amount of 16.233 oz to ensure that only 1% of the boxes contain less than 16oz of cereal. This is calculated by manipulating the confidence interval for a normal distribution and using the z-score for 99%.
  • #1
USN2ENG
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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
 
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  • #2
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

Your reasoning and your answer are correct.
 
Last edited:
  • #3
Thanks, Dr. Vickson
 

FAQ: Interval for a normal distribution

1. What is an interval for a normal distribution?

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.

2. How is the interval for a normal distribution calculated?

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.

3. What is the significance of the interval for a normal distribution?

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.

4. Can the interval for a normal distribution be used for any type of 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.

5. How does the interval for a normal distribution change with different confidence levels?

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.

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