Fit a normal curve to the following data :

Class Intervals	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	Total
Frequency	$2$	$11$	$24$	$33$	$20$	$8$	$2$	$100$

 

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?

In $\mathrm{N}(\mathrm{\mu },{\mathrm{\sigma }}^2)$ the value of $\mathrm{P}(\left|\mathrm{X}-\mathrm{\mu }\right|<2\mathrm{\sigma })$ is 

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

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 of the students are given below.

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

A factory employing a huge number of workers find that over a period of time, average absentee rate is three workers per shift. Calculate the probability that in a given shift more than $4$ workers will be absent?(Answer up to two decimal values)

A factory employing a huge number of workers find that over a period of time, average absentee rate is three workers per shift. Calculate the probability that in a given shift exactly $2$ workers will be absent.(Answer up to three decimal values)

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

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 $100\}$

The remuneration paid to $100$ lecturer coaching for professional entrance examination are normally distributed with mean $₹700/-$ and standard deviation $₹50/-$. Estimate the number of lectures whose remuneration is more than $₹750/-$

If$X~N\left(6,1.2\right)$ and $P(0<Z<1)$ $=0.3413$ then $P(4.8<X<7.2)$ is

A square is inscribed in a circle. If $p_1$ is the probability that a randomly chosen point of the circle lies within the square and $p_2$ is the probability that the point lies outside the square, then