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The average student loan debt for college graduates is $25,600
The average student loan debt for college graduates is $25,600. Suppose that that distribution is normal and that the standard deviation is $14,050. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.
a. What is the distribution of X? X ~ N(_____,_______)
b Find the probability that the college graduate has between $16,300 and $31,400 in student loan debt.
c. The middle 30% of college graduates' loan debt lies between what two numbers?
Low: $___
High: $___
Please show it to me how you use the T1 84 calculator for this.
Expert Solution
(a) X ~ N (25600, 14050)
(b) 0.4061
(c) Low: $20186
High: $31014
Step-by-step explanation
We have mean μ = 25600 and standard deviation σ = 14050
(a) We know that X follows a normal distribution with X ~ N(μ, σ)
setting the values, we get
X ~ N (25600, 14050)
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(b) Using TI 84 calculator
press 2nd button then VARS and select normalcdf
Lower = 16300
Upper = 31400
μ = 25600
σ = 14050
press calculate twice, we get
P(16300 < X < 31400) = normalcdf(16300, 31400, 25600, 14050) = 0.4061
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(c) We know that middle 30% is between 35th percentile and 65th percentile (because 65-35 = 30)
Using TI 84 calculator
press 2nd button then VARS and select invNorm
area = 0.35
μ = 25600
σ = 14050
press calculate twice, we get
35th percentile = invNorm(0.35, 25600, 14050) = 20186.2474 or 20186
Using TI 84 calculator
press 2nd button then VARS and select invNorm
area = 0.65
μ = 25600
σ = 14050
press calculate twice, we get
65th percentile = invNorm(0.65, 25600, 14050) = 31013.7526 or 31014
Therefore, Low: $20186 High: $31014
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