The mean and standard deviation of 75 observations are 45 and 10, respectively. If 2 is added to each observation, the new mean and standard deviation will be

Correct option is C

Adding a constant value to each observation in a data set will shift the mean by the same constant value but will not change the standard deviation.
Here's the breakdown:
 Original mean: 45
 Value added: 2
 New mean: Original mean + value added = 45 + 2 = 47
The standard deviation represents the spread of the data around the mean. Adding a constant value to each data point simply shifts the entire dataset together, maintaining the same relative distances between the points. Therefore, the standard deviation remains the same.
 Original standard deviation: 10
 New standard deviation: Remains the same = 10
Therefore, the new mean will be 47 and the new standard deviation will be 10.