The number of telephone calls made daily in a certain community between 8 P.M. and 9 P.M. has a mean of 352 and standard deviation of 31. What percentage of time will there be more than 400 telephone calls made in this community between 8 P.M. to 9 P.M.?

[Given that: $P(0\leq Z\leq1.55)=0.4394$, where $Z$ is the standard normal variate]

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$.

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

Choose the correct answer from the options given below:

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

If the probability distribution of X is :

Then variance is equal to :

A traffic police officer records the number of motorcycle riders that use a particular lane on a highway. He records that an average of 2.5 motorcycle riders use the lane every hour. Given that the number of motorcycles that use the particular lane follows a Poisson distribution. The probability that less than 2 motorcycle riders will use the lane within an hour will be:- (Use $e^{2.5} = 12.2$)