If you throw a coin in a vending machine, the coin is being weighed by the machine to determine its value. For statistical purposes, you decide to throw $10$ fifty-cent coins in vending machine A. This results in a sample mean of $7.49$ $g$ and a sample variance of $0.011$ $g^2$. You may assume a normal distribution as model distribution for the measurements.
Construct a $95%$ confidence interval for the mean weight $μ_A$ of a fity-cent coin thrown in machine $A$.
In this exercise, you'll use the student distribution or the standard normal distribution to construct the confidence interval? I know that they say 'You may assume a normal distribution as model distribution for the measurements' but they also give you the sample variance (that is used with the student distribution) and not the variance. Furthermore, $n=10$ is quite small, so, in my opinion, I should use the student distribution, it's correct?