According to the IRS the mean tax refund for the year 2009 w

According to the IRS the mean tax refund for the year 2009 was $3333.

The standard deviation of the population of returns is $551, and the amounts follow the normal distribution. Using Normal Distribution.

Mean = u = 3333
SD = 551

a) More than 2000 :

x = 2000

z = (x - u) / SD

z = (2000 - 3333) / 551

z = -2.4192377495462795

P(z > -2.4192377495462795) = 0.9922

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b) More than 5000 :

z = (5000 - 3333) / 551

z = 3.0254083484573503

P(z > 3.0254083484573503) = 0.0012 ----> ANSWER

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c) Between 3000 and 5000 :

z = (3000 - 3333) / 551
z = -0.6043557168784029
P(z < -0.6043557168784029) = 0.2728

z = (5000 - 3333) / 551
z = 3.0254083484573503
P(z < 3.0254083484573503) = 0.9988

P(3000 to 5000) = 0.9988 - 0.2728 = 0.726 ---> ANSWER

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