A random sample of n measurements was selected from a population with unknown mean µ and known standard deviation ?. Calculate a 95% confidence interval for µ for the given situation.
Round to the nearest hundredth when necessary.

$\mathrm { n } = 100 , \overline { \mathrm { x } } = 74 , \sigma = 25$

A) $74 \pm 0.49$
B) $74 \pm 4.11$
C) $74 \pm 4.9$
D) $74 \pm 49$

Question

A random sample of n measurements was selected from a population with unknown mean µ and known standard deviation ?. Calculate a 95% confidence interval for µ for the given situation.
Round to the nearest hundredth when necessary.

$\mathrm { n } = 100 , \overline { \mathrm { x } } = 74 , \sigma = 25$

A) $74 \pm 0.49$
B) $74 \pm 4.11$
C) $74 \pm 4.9$
D) $74 \pm 49$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula $\overline{x} \pm z \frac{\sigma}{\sqrt{n}}$. With $z \approx 1.96$, the interval is $74 \pm 1.96 \times \frac{25}{\sqrt{100}} = 74 \pm 4.9$.

A Random Sample of N Measurements Was Selected from a Population