Last year, the typical college student graduated with $27,600 in debt (The Bosto
ID: 3378863 • Letter: L
Question
Last year, the typical college student graduated with $27,600 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $8,000. Use Table 1.
What is the probability that the average debt of five recent college graduates is more than $20,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
What is the probability that the average debt of five recent college graduates is more than $25,000? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
Last year, the typical college student graduated with $27,600 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $8,000. Use Table 1.
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 20000
u = mean = 27600
n = sample size = 5
s = standard deviation = 8000
Thus,
z = (x - u) * sqrt(n) / s = -2.12
Thus, using a table/technology, the right tailed area of this is
P(z > -2.12 ) = 0.982996977 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 25000
u = mean = 27600
n = sample size = 5
s = standard deviation = 8000
Thus,
z = (x - u) * sqrt(n) / s = -0.73
Thus, using a table/technology, the right tailed area of this is
P(z > -0.73 ) = 0.767304908 [ANSWER]
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