SOLUTION: The average credit card debt of college seniors is $3962. If the debt is normally distributed with a standard deviation of $950, find these probabilities: a) What is the probabili

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Question 872391: The average credit card debt of college seniors is $3962. If the debt is normally distributed with a standard deviation of $950, find these probabilities:
a) What is the probability that a randomly selected senior owes at least $1000?


b) The 10% of seniors that owe the most money owe more than what amount?


c) 95% of all seniors owe how much debt (centered about the mean)?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x value the mean) 50% of the area under the curve is to the left 

and %50 to the right



Population: mean = 3962, SD = 950

a) P(x ≥ 1000) = -2962/950 = -3.118

   P(z > -3.118) = normalcdf( -3.118, 10) = .9991  0r 99.91%

b) invNorm(.90) = 1.28,   1.28*950 + $3962 = $5178 (10% owe more than this)

c) As a Rule: 2SD on either side of mean: is 95% of the Population

   3962 - 2*950 < x < 3962 + 2*950



For the normal distribution: 

one  standard deviation from the mean accounts for about 68% of the set 

two standard deviations from the mean account for about 95%

and three standard deviations from the mean account for about 99.7%.