Respuesta :
$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 = Ī¼ = $490,000
Standard deviation of retirement accounts = Ļ = Ā $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. Ā
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 :
https://brainly.com/question/28021875
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