Question

In: Statistics and Probability

The average student loan debt for college graduates is $25,300. Suppose that that distribution is normal...

The average student loan debt for college graduates is $25,300. Suppose that that distribution is normal and that the standard deviation is $11,250. 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 $7,500 and $18,100 in student loan debt.

c. The middle 30% of college graduates' loan debt lies between what two numbers?
     Low: $
     High: $

Solutions

Expert Solution

Solution :

Given that ,

mean = = $25300

standard deviation = = $11250

a.

X N (25300 , 11250)

b.

P($7500 < x < $18100) = P[(7500 - 25300)/ 11250) < (x - ) /  < (18100 - 25300) / 11250) ]

= P(-1.58 < z < -0.64)

= P(z < -0.64) - P(z < -1.58)

= 0.2611 - 0.0571

= 0.2040

Probability = 0.2040

c.

Middle 30%

Middle 30% thr z value are

= 1 - 30% = 1 - 0.3 = 0.7

/ 2 = 0.7 / 2 = 0.35

1 - / 2 = 1 - 0.35 = 0.65

z 0.35 = -0.3853

z 0.65 = 0.3853

Using z-score formula,

x = z * +

x = -0.3853 * 11250 + 25300 = 20965

and

x = 0.3853 * 11250 + 25300 = 29635

Two numbers are Low: $20965 High: $29635


Related Solutions

The average student loan debt for college graduates is $25,300. Suppose that that distribution is normal...
The average student loan debt for college graduates is $25,300. Suppose that that distribution is normal and that the standard deviation is $14,700. 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 $7,950 and $25,200 in student loan debt. c. The...
The average student loan debt for college graduates is $25,850. Suppose that that distribution is normal...
The average student loan debt for college graduates is $25,850. Suppose that that distribution is normal and that the standard deviation is $13,750. 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 $28,750 and $46,650 in student loan debt. c. The...
Student Debt – Vermont: The average student loan debt of a U.S. college student at the...
Student Debt – Vermont: The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $21,800. You take a random sample of 141 college students in the state of Vermont and find the mean debt is $23,000 with a standard deviation of $2,800. You want to construct a 99% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the...
Student Debt – Vermont: The average student loan debt of a U.S. college student at the...
Student Debt – Vermont: The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,500. You take a random sample of 146 college students in the state of Vermont and find the mean debt is $23,500 with a standard deviation of $2,600. We want to construct a 90% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the...
According to an estimate, the average total parent and student debt for new college graduates was...
According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010–11 (Time, October 31, 2011). A random sample of 500 of this year’s graduates showed that their average such debt is $39,000 with a standard deviation of $5500. Do the data provide significant evidence at a 3% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both the p-value approach...
The average student loan debt of a U.S. college student at the end of four years...
The average student loan debt of a U.S. college student at the end of four years of college is estimated to be about $22,000. You take a random sample of 150 college students in the state of Wyoming and find that the mean debt is $19,850, and the sample standard deviation is $2,180. (a) Construct a 95% confidence interval for the mean debt of all Wyoming college graduates. (b) Construct a 98% confidence interval for the mean debt of all...
The average student loan debt of a U.S. college student at the end of four years...
The average student loan debt of a U.S. college student at the end of four years of college is estimated to be about $22,000. You take a random sample of 150 college students in the state of Wyoming and find that the mean debt is $19,850, and the sample standard deviation is $2,180. (a) Construct a 95% confidence interval for the mean debt of all Wyoming college graduates. (b) Construct a 98% confidence interval for the mean debt of all...
The average student loan debt of a U.S. college student at the end of 4 years...
The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $23,300. You take a random sample of 136 college students in the state of Vermont and find the mean debt is $24,500 with a standard deviation of $2,700. You want to construct a 99% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the mean debt of all...
The average student loan debt of a U.S. college student at the end of 4 years...
The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $24,100. You take a random sample of 136 college students in the state of Vermont and find the mean debt is $25,000 with a standard deviation of $2,400. We want to construct a 90% confidence interval for the mean debt for all Vermont college students. (a) What is the point estimate for the mean debt of all...
A recent study of debt among college graduates reported that the average debt accumulated by graduates...
A recent study of debt among college graduates reported that the average debt accumulated by graduates of private colleges was ​$37,400​, with a sample standard deviation of ​$2,068​, while the average debt accumulated by graduates of public colleges was ​$11,800​, with a sample standard deviation of ​$2,101. The sample sizes were 70 and 180​, respectively. Complete parts a and b below. A. what is the test statistic? Use a significance level of 0.10 B. what is the p value
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT