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GrogVix [38]
3 years ago
7

A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real esta

te properties is normally distributed with a mean of $225,000 and a standard deviation of $50,000. Use a calculator to find how much money separates the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings.
Mathematics
1 answer:
Pachacha [2.7K]3 years ago
6 0

Answer:

The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Step-by-step explanation:

Let the random variable <em>X</em> represent the amount of money that the family has invested in different real estate properties.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = $225,000 and <em>σ</em> = $50,000.

It is provided that the family has invested in <em>n</em> = 10 different real estate properties.

Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:

\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39

Now the lowest 80% of the amount invested can be represented as follows:

P(\bar X

The value of <em>z</em> is 0.84.

*Use a <em>z</em>-table.

Compute the value of the mean amount invested as follows:

\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}

   =225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57

Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

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