I have the following problem:
Suppose that the number of hits on a website is a normal distribution with an average of 100 hits/day and a standard deviation of 10 hits/day. We take a random sample of 25 days and we calculate the average. We do this with more samples. What is the probaility of obtaining and average higher than 103 ?
So i understand that i have the following data:
average=100
deviation=10
sample size= 25 days
How do i resolve this problem ?
If $X\sim N(\mu,\sigma^2)$, then for a random sample of size $n$, the distribution of the mean $\bar{X}$ of the sample is $$\bar{X}\sim N(\mu,\frac{\sigma^2}{n})$$
So in this case, $$\bar{X}\sim N(100,4)$$ and you want to find $p(\bar{X}>103)$.
Can you finish?