Question 1178027
sample size = 30
population standard deviation = .25
sample mean = 3.5


standard error = population standard deviation / square root of sample size = .25/sqrt(30) = .0456435465.


z-score of two tail confidence interval of 90% = plus or minus 2.5758.


z-score formula = (x - m) / se


x is raw score
m is mean
se is standard error.


plus side raw score = .25/sqrt(30) * 2.5758 + 3.5 = 3.617568647
minus side raw score = .25/sqrt(30) * -2.5758 + 3.5 = 3.382431353



at 99% two tail confidence interval, the average amount of cheese injected will be between 3.6176 and 3.3824 grams.


visually, this looks like this:


<img src = "http://theo.x10hosting.com/2021/040401.jpg">


when you're dealing with the mean of a sample, you have to use the standard error rather than the standard deviation.