In a Mathematics test,the average marks of boys is $x \%$ and the average marks of girls is $y \%$ with $x \neq y$. If the average marks of all students is $z \%$,the ratio of the number of girls to the total number of students is

For a distribution with equal class widths,the median of $100$ observations is $25$. If the median class is $20-30$ and the number of observations less than $20$ is $45$,what is the frequency of the median class?

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

Let $y_1, y_2, y_3, \dots, y_n$ be $n$ observations. Let $w_i = l y_i + k$ for all $i = 1, 2, 3, \dots, n$,where $l$ and $k$ are constants. If the mean of $y_i$ is $48$ and their standard deviation is $12$,and the mean of $w_i$ is $55$ and their standard deviation is $15$,then the values of $l$ and $k$ are:

The average weight of students in a class of $35$ students is $40 \ kg$. If the weight of the teacher is included,the average weight increases by $0.5 \ kg$. The weight of the teacher is.....$kg$.

An analysis of monthly wages paid to the workers of two jute mills $A$ and $B$ gives the following data:

Metric	Mill-$A$	Mill-$B$
No. of workers	$500$	$600$
Average daily wage (in rupees)	$186$	$175$
Variance of distribution of wages	$81$	$100$

Then: