JEE Main 2013 — Probability & Statistics

If the median and the range of four numbers $\{x, y, 2 x+y, x-y\}$, where $0 < y < x < 2 y$, are 10 and 28 respectively, then the mean of the numbers is :

In a set of $2 n$ observations, half of them are equal to ' $\mathrm{a}$ ' and the remaining hall are equal to ' $-\mathrm{a}^{\prime}$ '. If the standard deviation of all the observations is 2 ; then the value of $|a|$ is :

Mean of 5 observations is 7 . If four of these observations are $6,7,8,10$ and one is missing then the variance of all the five observations is :

The mean of a data set consisting of 20 observations is 40 . If one observation 53 was wrongly recorded as 33 , then the correct mean will be:

The probability of a man hitting a target is $\frac{2}{5}$. He fires at the target $k$ times $(k$, a given number). Then the minimum $k$, so that the probability of hitting the target at least once is more than $\frac{7}{10}$, is :

$\mathrm{A}, \mathrm{B}, \mathrm{C}$ try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are $\frac{3}{4}, \frac{1}{2}, \frac{5}{8}$. The probability that the target is hit by A or B but not by $\mathrm{C}$ is :