For the most recent year available, the mean annual cost to attend a private university in the United States was $20,082. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.
Ninety-five percent of all students at private universities pay less than what amount? (
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To find the amount that 95% of all students at private universities pay less than, we can use the concept of z-scores and the cumulative distribution function (CDF) of the normal distribution.
Step 1: Calculate the z-score
The z-score formula is given by:
z = (x - μ) / σ
Where:
x = value we are interested in
μ = mean annual cost ($20,082)
σ = standard deviation ($4,500)
For the 95th percentile, we need to find the corresponding z-score. The z-score corresponding to the 95th percentile is approximately 1.645.
Step 2: Calculate the value using the z-score
Now, we can use the z-score to find the corresponding value using the formula:
x = μ + (z * σ)
Plugging in the values:
x = $20,082 + (1.645 * $4,500)
Calculating:
x ≈ $27,810.25
Therefore, 95% of all students at private universities pay less than approximately $27,810.25.
To find the amount that 95% of students pay less than, we need to calculate the z-score associated with that percentile and use it to find the corresponding value from the normal distribution. Here's how you can do this:
Step 1: Find the z-score
The z-score represents the number of standard deviations a particular value is from the mean. To find the z-score associated with the 95th percentile, we can use a standard normal distribution table or an online calculator.
The z-score associated with the 95th percentile is approximately 1.645.
Step 2: Calculate the amount
Once we have the z-score, we can calculate the amount using the formula:
Amount = Mean + (z-score * Standard Deviation)
In this case, the mean annual cost is $20,082 and the standard deviation is $4,500. Plugging in the values:
Amount = $20,082 + (1.645 * $4,500)
Calculating this expression, we can find the amount that 95% of students pay less than.
For the most recent year available, the mean annual cost to attend a private university in the United States was $20,082. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.
Ninety-five percent of all students at private universities pay less than what amount?