Answer:
a) To find the value of x when the mean is 1.8, you can use the formula for the mean (average):
\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} \]
Given that the mean is 1.8 and the number of students is 2, x, 3, 4, 1, you can set up the equation:
\[ 1.8 = \frac{2 + x + 3 + 4 + 1}{5} \]
Solve for x to find its value.
b) If the mean of the distribution is 2, you can set up the equation:
\[ 2 = \frac{2 + x + 3 + 4 + 1}{5} \]
Solve for x to find the possible value.
c) If the mode is 3, the mode is the value that appears most frequently. In this case, 3 is the mode. To maximize the value of x, you would want to have as many occurrences of 3 as possible. Therefore, x should also be 3. So, the greatest possible value of x is 3.