Private nonprofit four-year colleges charge, on average, $26,599 per year in tuition and fees. The standard deviation is $7,230. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( 26,599 7,230 b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 29,531 per year. c. Find the 61th percentile for this distribution. $ (Round to the nearest dollar.)

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**Private Nonprofit Four-Year College Tuition Analysis**

Private nonprofit four-year colleges charge, on average, $26,599 per year in tuition and fees. The standard deviation is $7,230. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.

**a. Distribution Analysis**
What is the distribution of X?
- \( X \sim N(26,599, 7,230) \)

**b. Probability Calculation**
Find the probability that a randomly selected private nonprofit four-year college will cost less than $29,531 per year.
- [Answer Box Provided for Calculation]

**c. Percentile Calculation**
Find the 61st percentile for this distribution. Round to the nearest dollar.
- [Answer Box Provided for Calculation]
Transcribed Image Text:**Educational Website Content:** **Private Nonprofit Four-Year College Tuition Analysis** Private nonprofit four-year colleges charge, on average, $26,599 per year in tuition and fees. The standard deviation is $7,230. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. **a. Distribution Analysis** What is the distribution of X? - \( X \sim N(26,599, 7,230) \) **b. Probability Calculation** Find the probability that a randomly selected private nonprofit four-year college will cost less than $29,531 per year. - [Answer Box Provided for Calculation] **c. Percentile Calculation** Find the 61st percentile for this distribution. Round to the nearest dollar. - [Answer Box Provided for Calculation]
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