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 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.
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Answers (1)

oldgaffer1b
Answered 2022-09-30 Author has 9 answers
Step 1
We know the population standard deviation σ = 0.7 so we can find z∗ by:
z = Φ 1 ( 1 α 2 )
Step 2
As we want a 95% confidence level we have α = 0.05, this means z = 1.96. We also know the population mean μ = 2.8 so we can get the confidence interval by plugging in the values (including n = 100):
( μ z σ n , μ + z σ n ) = ( 2.6628 , 2.9372 )
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