The random variable $X$ has mean $30$ and variance $36$. The random variable $\overline{X}$ is the mean of a random sample of $100$ observations of $X$. State the approximate distribution of $\overline{X}$, giving its parameters, and find the probability that the sample mean is greater than $31$.

Which of the following is not true regarding the normal distribution?

Find the mean and standard deviation of the normal distribution in which $8\%$ items are under $72$ and $99\%$ are over $53$.

A normal distribution has mean $150$ and S.D $10$. Find the limits between which the middle $60\%$ of the values lie.

The Education department conducts a coaching program. The scores got by the students in the examinations after the coaching program were normally distributed and the Z scores for some of the students are given below.

Which of these students scored above the mean?

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

In a continuous distribution the p.d.f of $\mathrm{X}$ is :

$\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{cc}\frac{3\mathrm{x}(2-\mathrm{x})}{4}& 0<\mathrm{x}<2\\ 0& \mathrm{elsewhere}\end{array}\right.$ Find the mean and variance.

The Education department conducts a coaching program. The scores got by the students in the examinations after the coaching program were normally distributed and the Z scores for some students are given below.

Which of these students scored below the mean?

The Education department conducts a coaching program. The scores got by the students in the examinations after the coaching program were normally distributed and the Z scores for some of the students are given below.

If the mean score is $150$ and S.D is $20$. What is the score of each student?