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Uptown Country Club only admits members with annual incomes in the top 2.5% of the United States. If the annual individual income in the US has a mound-shaped symmetrical distribution with a mean of $55,000 and a standard deviation of $10,000, what is the approximate minimum annual income required for admission to the country club?

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opudodennis

Answer:

$74,600

Step-by-step explanation:

-Given the probability is 2.5%, mean=$55,000 and standard deviation= $10,000

-We find the z value of 2.5%

[tex]p=P(z>\frac{X-\mu}{\sigma})\\\\1.96=P(z<\frac{X-\mu}{\sigma}}\\\\\\\therefore 1.96=\frac{X-55000}{10000}\\\\\\X=1.96\times 10000+55000\\\\=74600[/tex]

Hence, the minimum amount of income to be in the top 2.5% is $74,600

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