A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma =$ $19.0$ milligrams. Construct a $95 \%$ confidence interval for the true mean cholesterol content, $\mu$, of all such eggs.
A) $224 \mathrm { mg }

Question

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma =$ $19.0$ milligrams. Construct a $95 \%$ confidence interval for the true mean cholesterol content, $\mu$, of all such eggs.
A) $224 \mathrm { mg } < \mu < 232 \mathrm { mg }$
B) $223 \mathrm { mg } < \mu < 231 \mathrm { mg }$
C) $225 \mathrm { mg } < \mu < 233 \mathrm { mg }$
D) $223 \mathrm { mg } < \mu < 232 \mathrm { mg }$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{\sigma}{\sqrt{n}}$. Here, $\bar{x} = 228$, $z \approx 1.96$, $\sigma = 19$, and $n = 82$. The interval is $228 \pm 1.96 \times \frac{19}{\sqrt{82}}$, which calculates to approximately $224 \mathrm{mg} < \mu < 232 \mathrm{mg}$.

A Laboratory Tested 82 Chicken Eggs and Found That the Mean