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

The answer is "0.0764"

Explanation:

Please find the complete question in the attached file.

`\to \mu = \$ \ 4064\\\\\to \sigma = \$ \ 460 \\\\\to \sigma \bar{x} = (\sigma)/(√(n))\\\\`

`= (460)/(√(21))\\\\ = (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\\\\`