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 the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

Two sets,each of $20$ observations,have the same standard deviation $5$. The first set has a mean $17$ and the second a mean $22$. Determine the standard deviation of the set obtained by combining the given two sets.

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...

One set containing five numbers has mean $8$ and variance $18$,and the second set containing $3$ numbers has mean $8$ and variance $24$. Then the variance of the combined set of numbers is

If the sum of the deviations of $50$ observations from $30$ is $50$,then the mean of these observations is: