Question

Medicare Hospital Insurance The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. Suppose the benefits are normally distributed with a standard deviation of $460. Round the final answers to at least four decimal places and intermediate z-value calculations to two decimal places.

Answer 1

Answer:

The answer is "0.0764"

Step-by-step explanation:

Please find the complete question in the attached file.

$\to \mu = \ \ 4064\\\\\to \sigma = \ \ 460 \\\\\to \sigma \bar{x} = \frac{\sigma}{\sqrt{n}}$

        $= \frac{460}{\sqrt{21}}\\\\ = \frac{460}{4.58257569}\\\\=100.3802$

$\to P(\bar{x}< \ \ 3920) = \frac{P((\bar{x} - \mu \bar{x})}{\frac{\sigma \bar{x}<(3920 - 4064)}{100.3802)}}$

$\to P(z < -1.43) = 0.0764 \\\\\to P(\bar{x}< \ \ 3920) = 0.0764$