Answer :
$484,835 is the amount that separates the lowest 20% of the means of retirement accounts from the highest 80% of the means of retirement accounts.
Given Information:
Mean of retirement accounts = μ = $490,000
Standard deviation of retirement accounts = σ = $55,000
Sample size = n = 80
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The amount of money that separates the lowest 20% of the means of retirement accounts from the highest 80% is given by
[tex]P\frac{( \bar x - \alpha )}{\frac{\sigma}{\sqrt{n} } }[/tex]
The z-score corresponding to 0.20 is -0.84
[tex]\bar x = \alpha + z.\frac{\sigma }{\sqrt{n} } \\\\\bar x = 490,000 - 0.84 .\frac{55,000}{\sqrt{80} } \\\\\bar x = 490,000 - 5165.32\\\\\bar x = 484,834.68[/tex]
Rounding off to the nearest whole number
[tex]\bar x = $484,835[/tex]
Therefore, $484,835 is the amount that separates the lowest 20% of the means of retirement accounts from the highest 80% of the means of retirement accounts.
How to use z-table?
In the z-table find the probability of 0.20
Note down the value of that row, it would be -0.8.
Note down the value of that column, it would be 0.04.
So the z-score is -0.84
Learn more about Probability Distribution at :
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