An anti-aircraft gun takes a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first,second,third,and fourth shot are $0.4, 0.3, 0.2$,and $0.1$ respectively. The probability that the gun hits the plane is

The mean and variance of the marks obtained by $n$ students in a test are $10$ and $4$ respectively. Later,the marks of one of the students is increased from $8$ to $12$. If the new mean of the marks is $10.2$,then their new variance is equal to:

If for some $x \in R^{+} \cup \{0\}$,the frequency distribution of the marks obtained by $20$ students in a test is given by the table below,then find the mean of the marks.

Marks:	$2$	$3$	$5$	$7$
Frequency:	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean,mode and variance of $n$ observations $x_1, x_2, ..., x_n$ and $d_i = -x_i - a, i = 1, 2, ..., n$,where $a$ is any number. Statement $I$: Variance of $d_1, d_2, ..., d_n$ is $\sigma^2$. Statement $II$: Mean and mode of $d_1, d_2, ..., d_n$ are $-\bar{x} - a$ and $-M - a$,respectively.

The coefficients of variation of two distributions are $60$ and $70$. The standard deviations are $21$ and $16$ respectively. Find their means.

The mean of a data set comprising $16$ observations is $16$. If one observation with value $16$ is deleted and three new observations with values $3, 4,$ and $5$ are added to the data,then the mean of the resultant data is: