Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 25,096 per year. c. Find the 61th percentile for this distribution. $ (Round to the nearest dollar.)

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**Distribution of Tuition Costs in Private Nonprofit Four-Year Colleges**

Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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?**  
   \( X \sim N(\text{mean}, \text{standard deviation}^2) \)

b. **Find the probability that a randomly selected Private nonprofit four-year college will cost less than $25,096 per year.**  
   (Enter the calculated probability in the provided space)

c. **Find the 61st percentile for this distribution.**  
   \( \$ \text{(Enter the calculated amount rounded to the nearest dollar)} \)
Transcribed Image Text:**Distribution of Tuition Costs in Private Nonprofit Four-Year Colleges** Private nonprofit four-year colleges charge, on average, $26,059 per year in tuition and fees. The standard deviation is $7,129. 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?** \( X \sim N(\text{mean}, \text{standard deviation}^2) \) b. **Find the probability that a randomly selected Private nonprofit four-year college will cost less than $25,096 per year.** (Enter the calculated probability in the provided space) c. **Find the 61st percentile for this distribution.** \( \$ \text{(Enter the calculated amount rounded to the nearest dollar)} \)
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Mean=26059

Standard deviations=7129

 

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