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
The standard error would just therefore be equal to
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.
ANSWER: 417.1<μ<482.9
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
The standard error would just therefore be equal to
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.
ANSWER: 417.1<μ<482.9