A distribution of scores has a mean of µ = 50. One new score is added to the distribution and the new mean is found to be µ = 48. From this result, you can conclude that the new score was ____.​Group of answer choices​less than 50​greater than 50​equal to 48​between 50 and 52

To determine the new score added to the distribution, we can use the information given about the means before and after the new score was added.

1. Let $N$ be the number of scores in the original distribution.
2. The original mean is $\mu = 50$, so the total sum of the original scores is $50N$.
3. After adding one new score $X$, the new mean becomes $\mu = 48$.
4. The new total number of scores is $N + 1$.
5. The new total sum of the scores is $50N + X$.

Using the formula for the mean: $\text{New mean} = \frac{\text{New total sum}}{\text{New total number of scores}}$

Substitute the given values: $48 = \frac{50N + X}{N + 1}$

To find $X$, solve the equation step by step:

1. Multiply both sides by $N + 1$: $48(N + 1) = 50N + X$

2. Distribute 48 on the left side: $48N + 48 = 50N + X$

3. Subtract $48N$ from both sides: $48 = 2N + X$

4. Isolate $X$: $X = 48 - 2N$

Since $N$ is a positive integer, $2N$ is a positive number. Therefore, $48 - 2N$ will be less than 48.

Thus, the new score $X$ was less than 48.