Question

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.

Answer 1

`226.69,233.31`

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,

`\text{Sample size}=n=90\\\\\text{Mean}=\mu=230\\\\\text{Standard deviation}=\sigma=16`

we know that, confidence interval is,

`\mu\pm Z\left((\sigma)/(√(n))\right)`

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

`=230\pm 1.96\left((16)/(√(90))\right)`

`=230\pm 3.31`

`=226.69,233.31`

Answer 2

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)