The sum of two positive integers is $100$. The probability that their product is greater than $1000$ is

The mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were incorrectly recorded as $91$ and $13$. The correct mean is...

Let $a, b, c \in N$ and $a < b < c$. Let the mean,the mean deviation about the mean,and the variance of the $5$ observations $9, 25, a, b, c$ be $18, 4$,and $\frac{136}{5}$,respectively. Then $2a + b - c$ is equal to:

The $A.M.$ of $n$ observations is $M$. If the sum of $n - 4$ observations is $a$,then the mean of the remaining $4$ observations is:

What is the weighted mean of the first $n$ natural numbers when the weights are equal to the corresponding natural numbers?

The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking,it was found that an observation was read as $10$ in place of $12$. If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively,then $15(\mu+\mu^2+\sigma^2)$ is equal to $...................$