sample mean to population mean

Question

How to use sample mean to know the population mean? Now I have sample mean, sd and population mean. They are 37.28, 25 and 34. Sample size is 25 Here is my thought N < 25. Sample mean may not equal to population mean. population mean is 37.28 + 25/√25 =42 Am i correct?

Answer 1

Hint: The $1-\alpha$ confidence interval for $\mu$ is

$$\large{\left[ \overline X-z_{(1-\frac{\alpha}{2})} \cdot \frac{\sigma}{\sqrt n} , \overline X+z_{(1-\frac{\alpha}{2})} \cdot \frac{\sigma}{\sqrt n}\right]}$$

$z_{(1-\frac{\alpha}{2})}$ is the z-value of the standard normal distribution. $1-\alpha$ is the confidence level.

In your case $\overline X=37.28$, $\sigma=34$ and $1-\frac{\alpha}{2}=1-\frac{0.01}{2}=0.995$