Normal Curve Item

Scenario: It is assumed that college students attending HBCU schools have an estimated average student loan debt of $40,000 and a standard deviation of $7,000, which follows a normal distribution. You may use the shorthand notation, X ~ n(40, 7). Use this information to answer the following questions. Show all work in the yellow section provided and turn in your work to me by noon tomorrow, Friday, 26 March 2021. ALSO, PROVIDE A CORRECT INTERPRETATION. EXPAND THE YELLOW WORK SECTION AS NEEDED.

VSU PSYC 315-01 Quantitative Methods Graded Exercise NAME: ________________________ Dr. Kenneth W. Lewis, Psychology (180 PTS) DATE: ________________________

Scenario: It is assumed that college students attending HBCU schools have an estimated average student loan debt of $40,000 and a standard deviation of $7,000, which follows a normal distribution. You may use the shorthand notation, X ~ n(40, 7). Use this information to answer the following questions. Show all work in the yellow section provided and turn in your work to me by noon tomorrow, Friday, 26 March 2021. ALSO, PROVIDE A CORRECT INTERPRETATION. EXPAND THE YELLOW WORK SECTION AS NEEDED. This is directly from our class work so, no exceptions for late work will be offered.

SPECIAL INSTRUCTIONS: TO ADJUST THE SIZE OF THE YELLOW WORK BOX, CLICK ON IT AND PULL DOWN ON THE BOTTOM CENTER CIRCLE THAT WILL APPEAR. YOU WILL SEE WHAT HAPPENS.

BEGIN WORK ON NEXT PAGE: X ~ n(40k, 7k).

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1. (10 PTS) Find P(X < $50K).

2. (12 PTS) Find P(X > $26K).

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3. (20 PTS) Find P($26K < X < $50K)

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4. (10 PTS) 36% of all student loan debt is lower than what loan amount, X?

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5. (12 PTS) 2% of all student loan debt is higher than what loan amount, X?

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6. (20 PTS) The middle 68 percent of all HBCU students have student loan debt that is between what two values of X1 and X2?

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7. (10 PTS) What percent of HBCU students have student loan debt that is within 2.34 standard deviations of the mean?

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8. (12 PTS) What percent of HBCU students have student loan debt that is BEYOND 1.60 standard deviations of the mean?

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9. (15 PTS) If the sample of HBCU students is n = 5000, how many HBCU students have student loan debt that is less than $50K?

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10. (14 PTS) If the sample of HBCU students is n = 5000, how many HBCU students have student loan debt that greater than $30k?

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11. (5 PTS) What is the coefficient of variation, CV, of this distribution?

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12. (10 PTS) Find the value of Xp95 in this distribution.

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13. (10 PTS) Find the value of Xp18 in this distribution.

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14. (20 PTS) What are the IQR and the lower and upper bounds of possible outliers of this distribution of HBCU student loan debt? Use the same procedures that we previously used to find this information.

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