Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25
These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.
A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.
Next, we look for the standard error of the mean. This will have a formula
[tex]error= \frac{standard deviation of population}{ \sqrt{N} } [/tex]
The standard error would just therefore be equal to
[tex] \frac{100}{ \sqrt{25} }= \frac{100}{5} =20[/tex]
Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
[tex]450-20(1.645)=417.1[/tex]
[tex]450+20(1.645)=482.9[/tex]
ANSWER: 417.1<μ<482.9
