The concentration of calcium in the blood for a given population follows a normal law of mean μ = 2.8 mmol / L and standard deviation σ = 0.7 mmol / L. If we take a sample of 100 people, what is the confidence interval of the calcium concentration at the 95% confidence level.
I got the confidence interval [2.663; 2.937] but I think this is wrong.
We know the population standard deviation $\sigma = 0.7$ so we can find $z^*$ by: $$ z^* = \Phi^{-1}(1-\frac{\alpha}{2}) $$ As we want a 95% confidence level we have $\alpha = 0.05$, this means $z^* = 1.96$. We also know the population mean $\mu = 2.8$ so we can get the confidence interval by plugging in the values (including $n=100$): $$ \left(\mu - z^* \frac{\sigma}{\sqrt{n}}, \mu + z^* \frac{\sigma}{\sqrt{n}} \right) = (2.6628, 2.9372) $$
I hope it helps :)