Let the correlation coefficient between X and Y be 0.6. Random variables Z and W are defined as Z = X + 5 and W = $${Y \over 3}$$. What is the correlation coefficient between Z and W ?

If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance on the resulting series?

The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?

Consider the following for the four (04) items that follow:
The frequency distribution of height of students of a class is given below:

Height (in cm	Number of Students
160-162	12
162-164	15
164-166	24
166-168	13

 

What is the total number of students whose height is less than or equal to 165 cm?