How to find Q1, given the mean and standard deviation.?

How to find Q1, given the mean and standard deviation.?

Postby morgan86 » Tue Feb 22, 2011 8:38 pm

Credit card debt for college seniors follows a Normal model with a mean of 5,000 and standard deviation fo 1,400.
If you can help me answer any of these questions it would help a lot.

a. What is the amount of credit card debt that represents Q1?

b. What percentage of college seniors have between 2000 and 4000 of credit card debt?

c. What percentage has over 6,000?

d. Find the 80th percentile for the amount of credit card debt for this group.
morgan86
 
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How to find Q1, given the mean and standard deviation.?

Postby abir45 » Tue Feb 22, 2011 8:39 pm

a. What is the amount of credit card debt that represents Q1?
P ( x < 4055.7143 ) = P ( z < -0.6745) = 0.25

b. What percentage of college seniors have between 2000 and 4000 of credit card debt?
z = ( x - ? ) / ?
P (2000 < x < 4000) = P (-2.1429 < z < -0.7143) = 0.2215

c. What percentage has over 6,000?
P (x > 6000) = P (z > 0.7143) = 0.2375

d. Find the 80th percentile for the amount of credit card debt for this group.
P ( x < 6178.2697 ) = P ( z < 0.8416) = 0.80
abir45
 
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