If the heights of 300 students are normally distributed with mean 68 inches and standard deviation 3 inches. If Z is the standard normal variate such that $P(0\le Z\le 1.33)=0.4082, P(Z\ge 1.33)=0.0918$ and $P(0\le Z\le 1)=0.3413$, then which of the following statements are correct?

(A) There are 27 students whose height is greater than 72 inches.

(B) The number of students having heights less than or equal to 64 inches is 27.

(C) 210 students have their heights between 65 and 71 inches.

(D) There are 35 students whose height is greater then 72 inches.

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If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is:

A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then

Match the LIST-I with LIST-II

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If the probability distribution of X is :

Then variance is equal to :

A random variable X has the following probability distribution:

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(C) $P(X=2)=0.30$

(D) $P(X \le 2)=0.55$

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The probability distribution of a random variable $X$ is given as $P(X=x)=\begin{cases}kx^3 & \text{for } x=1,2,3\\ 3kx & \text{for } x=4,5\\ 0 & \text{otherwise}\end{cases}$, where $k$ is a constant.

The value of $P(X\ge4)$ is

In a single throw of a die, if X denotes the number on its upper face, then the mean of X is,