# The confidence interval is [2.663;2.937]? The concentration of calcium in the blood for a given population follows a normal law of mean mu = 2.8 mmol / L and standard deviation sigma = 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.

Isaac Barry 2022-09-29 Answered
The confidence interval is [2.663;2.937]?
The concentration of calcium in the blood for a given population follows a normal law of mean $\mu =2.8$ mmol / L and standard deviation $\sigma =0.7$ 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.
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oldgaffer1b
Step 1
We know the population standard deviation $\sigma =0.7$ so we can find z∗ by:
${z}^{\ast }={\mathrm{\Phi }}^{-1}\left(1-\frac{\alpha }{2}\right)$
Step 2
As we want a 95% confidence level we have $\alpha =0.05$, this means ${z}^{\ast }=1.96$. We also know the population mean $\mu =2.8$ so we can get the confidence interval by plugging in the values (including $n=100$):
$\left(\mu -{z}^{\ast }\frac{\sigma }{\sqrt{n}},\mu +{z}^{\ast }\frac{\sigma }{\sqrt{n}}\right)=\left(2.6628,2.9372\right)$