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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250

feet and a standard deviation of 50 feet. We randomly sample 64 fly balls. Find the 70th percentile of the
distribution of the average of 49 fly balls.

User Marek Bar
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Answer: Let's assume that the employee initially invests an amount "x" in company stock. Since she wants to invest twice as much in the mutual fund, she will invest 2x in the mutual fund. The amount invested in bonds can be represented as (2000 - x - 2x) = (2000 - 3x), as the total investment in the three options must equal $2000.

Now, let's calculate the increase in value for each investment:

Increase in value of the mutual fund investment: 2x * 0.045 (4.5% increase)

Increase in value of the bonds investment: (2000 - 3x) * 0.026 (2.6% increase)

Decrease in value of the company stock investment: x * (-0.002) (0.2% decrease)

The total increase in value is given as $58:

2x * 0.045 + (2000 - 3x) * 0.026 - x * 0.002 = 58.

Now, let's solve for "x":

0.09x + 52 - 0.002x = 58

0.088x + 52 = 58

0.088x = 6

x = 6 / 0.088

x ≈ 68.182.

So, the employee initially invested approximately $68.18 in company stock.

Now, we can find the amounts invested in the mutual fund and bonds:

Amount invested in the mutual fund = 2x ≈ 2 * 68.182 ≈ 136.364.

Amount invested in bonds = 2000 - (68.182 + 136.364) ≈ 1795.454.

To summarize:

Amount initially invested in the mutual fund ≈ $136.36.

Amount initially invested in bonds ≈ $1795.45.

Amount initially invested in company stock ≈ $68.18.

User Ryan Fox
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