Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation?

Let X be a random variable following binomial distribution with parameters n = 5 and p = k Further, P(X = 1) = 0.4096 and P(X = 2) = 0.2048 . What is the value of k? 

The frequency distribution of the marks obtained by students in a Science examination is given below:
 

Marks	5-15	15-25	25-35	35-45
Number of students	20	30	30	20

What is the arithmetic mean?