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A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with italic sigma space equal space 16.0 milligrams. Construct a 95 percent confidence interval for the true mean cholesterol content, μ, of all such eggs.

Respuesta :

Given:
Sample size, n =90
Expected mean, μ = 230 mg
Standard deviation, σ = 16 mg

At 95% confidence interval, the true mean will lie in the interval
(μ + 1.96(σ/√n), μ - 1.96(σ/√n)
= (230 + (1.96*16)/√(90), 230 - (1.96*16)/√(90))
= (230 - 3.306, 230 - 3.306)
= (233.3, 226.7)   to nearest tenth

Answer:
The 95% confidence interval for the true mean is (233.3, 226.7)
 
InesWalston

Answer:

[tex]226.69,233.31[/tex]

Step-by-step explanation:

A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with standard deviation as 16.0 milligrams.

So here,

[tex]\text{Sample size}=n=90\\\\\text{Mean}=\mu=230\\\\\text{Standard deviation}=\sigma=16[/tex]

we know that, confidence interval is,

[tex]\mu\pm Z\left(\dfrac{\sigma}{\sqrt{n}}\right)[/tex]

For 95% confidence interval Z is 1.96, putting all the values,

[tex]=230\pm 1.96\left(\dfrac{16}{\sqrt{90}}\right)[/tex]

[tex]=230\pm 3.31[/tex]

[tex]=226.69,233.31[/tex]