A professor informs her class that a test is very difficult, but the grades will be curved. Scores for the test are normally distributed with a mean of 25 and a standards deviation of 5. If she curves the grades by adding 50 to each grade, What is the new mean? What is the new standard deviation?
The new mean will be 25+ 50 = ?
The standard deviation will remain the same.
The new mean is 75 (25 + 50); however the standard deviation stays at 5 because she adds the same amount of points to all grades, so the curve is just shifting up rather than changing shapes.
To find the new mean and standard deviation after curving the grades by adding 50 to each grade, we need to understand the properties of adding a constant value to a normally distributed random variable.
Adding a constant value does not affect the shape of the distribution; it only shifts the distribution to the right or left. In this case, adding 50 to each grade will shift the distribution to the right.
Step 1: Find the new mean
The new mean is obtained by adding the constant value (50) to the original mean (25).
New mean = original mean + constant value
New mean = 25 + 50 = 75
Step 2: Find the new standard deviation
The standard deviation remains the same when adding a constant value to a random variable. Therefore, the new standard deviation will be the same as the original standard deviation.
New standard deviation = original standard deviation = 5
In conclusion:
The new mean after curving the grades is 75, and the new standard deviation remains as 5.
To find the new mean and standard deviation after curving the grades, we need to understand the effect of adding a constant value to each grade on the mean and standard deviation of a normally distributed dataset.
When a constant value is added to each data point in a normally distributed dataset, the new mean will also increase by that constant value. However, the standard deviation remains the same because adding a constant value does not affect the spread or variability of the data.
Given that the original mean is 25 and the standard deviation is 5, and the professor curves the grades by adding 50 to each grade:
1. New Mean:
To find the new mean, we simply add the constant (50) to the original mean:
New Mean = Original Mean + Constant
New Mean = 25 + 50
New Mean = 75
Therefore, the new mean for the curved grades is 75.
2. New Standard Deviation:
Since adding a constant value does not affect the standard deviation, the new standard deviation remains the same as the original standard deviation.
New Standard Deviation = Original Standard Deviation
New Standard Deviation = 5
Therefore, the new standard deviation for the curved grades is also 5.