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You take random sample of 200 people from Salinas and find that their average income is $48,000 per year
with a standard deviation of $9000. Also assume that population incomes are normally distributed.
Approximately how many people make between $39,000 and $57,000?
X
Answer format: Enter a positive integer

Respuesta :

okpalawalter8

We have that the amount of people that makes between $39,000 and $57,000

[tex]X=28 People[/tex]

For normal distribution, P(X < A) = P(Z < (A - mean)/standard deviation)  

Mean = $48,000  

Standard deviation = $9000  

P(Person will have salary less than

[tex]P(39,000 < X < 57,000) = P(X < 35,000)-P(Z < (57,000 )[/tex]  

[tex]=P(Z < (57,000 - 48,000)/9,000) - P(Z < (35,000 - 48,000)/9,000)[/tex]  

[tex]= P(Z < 1) - P(Z < -2)\\\=0.1587-0.0228[/tex]

[tex]= 0.1359[/tex]

People in sample of 500 that make salary between

$35,000 and $57,000

[tex]X= 27.18[/tex]

[tex]X=28 People[/tex]

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= 409 people

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