Question 511 Mark
About which value is the standard normal symmetric?
Answer
View full question & answer→The standard normal curve is symmetric about $z = 0$ on both sides.
Questions · Page 2 of 2
1 Marks Each
Question 521 Mark
What is called the value of standard normal variable $Z?$
Answer
View full question & answer→The value of standard normal variable $z$ is called standard score or $Z-$score.
Question 531 Mark
State the formula to change normal random variable $X$ into standard variable $Z$ with parameters $\boldsymbol{\mu}$ and $\boldsymbol{\sigma}^2$ ?
Answer
View full question & answer→To change normal variable $X$ into standard normal variable $Z,$ the formula is $Z = \frac{x-\mu}{\sigma}$.
Question 541 Mark
Define normal variate.
Answer
View full question & answer→A random variable $X,$ the mathematical form of its probability density function $f(x)$ is as per the normal distribution is called a normal variable.
Question 551 Mark
State the interval for middle $95.45\%$ of observations of a data in normal curve.
Answer
View full question & answer→The interval for middle $95.45\%$ of observations of a data in normal curve is $\mu - 2 \sigma$ to $\mu + 2 \sigma $
Question 561 Mark
In normal distribution, what percentage of observations lies in the interval $\mu \pm 2.575 \sigma$ ?
Answer
View full question & answer→In normal distribution $99\%$ of observations of the distribution lie in the interval $\mu ± 2.575 \sigma .$
Question 571 Mark
State the area between $\boldsymbol{\mu} \pm \mathbf{2 \sigma}$ in normal curve.
Answer
View full question & answer→In normal curve the area between $\mu ± 2\sigma $ is $0.9545$
Question 581 Mark
State the probability that the normal variable assumes a value in the interval $(\boldsymbol{\mu}-\boldsymbol{\sigma} ; \boldsymbol{\mu}+\boldsymbol{\sigma})$ of the normal distribution.
Answer
View full question & answer→The probability that the normal variable assumes a value in the interval $(\mu - \sigma ; \mu + \sigma )$ is $0.6826$
Question 591 Mark
State the value of median in standard normal distribution.
Answer
View full question & answer→In standard normal distribution mean $(\mu)=$ median $(M)=\operatorname{Mode}\left(M_0\right)=0$.
Therefore value of median is $0 .$
Therefore value of median is $0 .$
Question 601 Mark
What is the value of mean and variance in standard normal distribution?
Answer
View full question & answer→In standard normal distribution mean $= 0$ and variance $= 1.$
Question 611 Mark
How is the probability curve in standard normal distribution?
Answer
View full question & answer→The probability curve is bell-shaped in standard normal distribution.
Question 621 Mark
When it is said that “Probability distribution is normal probability distribution”?
Answer
View full question & answer→If the curve of the probability density function of a random variable $X$ is bell shaped, then the probability distribution $X$ is called the normal distribution.
Question 631 Mark
Mean and variance of random variable $X$ are $\mu$ and 1 respectively, if $X$ is normal distribution then find the value of $P$ ( $X \geq \mu$ ) and $P(X \leq \mu)$
Answer
View full question & answer→Mean $= \mu$ and variance $= 1,$
therefore $P(x \geq \mu ) = 0.5$ and $P(x \leq \mu )= 0.5.$
therefore $P(x \geq \mu ) = 0.5$ and $P(x \leq \mu )= 0.5.$
Question 641 Mark
State the estimated values of quartile deviation and mean deviation in the standard normal distribution.
Answer
View full question & answer→In the standard normal distribution, $Q_1=\mu-0.675 \sigma$ and $Q_3=\mu+0.675$.
Question 651 Mark
What is the value of skewness of normal curve symmetric?
Answer
View full question & answer→The normal curve is asymptotic to $X-$axis.
Question 661 Mark
How is the normal curve on both the ends of $X-$axis?
Answer
View full question & answer→The normal curve is asymptotic to $X-$axis.
Question 671 Mark
Why is the total area of the region bounded by the normal curve and $X-$axis taken as $1?$
Answer
View full question & answer→The normal curve is a probability curve and total probability is $1.$
Hence, the total area of the region bounded by the normal curve and $X-$axis is taken as $1.$
Hence, the total area of the region bounded by the normal curve and $X-$axis is taken as $1.$
Question 681 Mark
What is the relation between measurements of central tendency in a normal distribution?
Answer
View full question & answer→In a normal distribution, measures of central tendency i.e. mean, median and mode are equal.
Question 691 Mark
What is the graph of probability density function?
Answer
View full question & answer→The graph of probability density function is bell-shape$(D).$
Question 701 Mark
For which variable, normal distribution is a probability distribution.
Answer
View full question & answer→Normal distribution is of continuous variable probability distribution.
Question 711 Mark
What is the value of variance and standard deviation in standard normal probability distribution?
Answer
View full question & answer→In standard normal probability distribution variance $=$ standard deviation $= 1.$
Question 721 Mark
Which type of values of $Z$ are left to perpendicular line at $Z=0?$
Answer
View full question & answer→The values of $Z$ left to perpendicular line at $Z = 0$ are negative.
Question 731 Mark
State the estimated value of $Q_1$ and $Q_3$ in standard normal distribution.
Answer
View full question & answer→In standard normal distribution $Q_1=-0.675$ and $Q_3=0.675$.
Question 741 Mark
Draw the graph of normal curve and locate the position of quartiles.
Answer
View full question & answer→Normal Probability Curve :
Question 751 Mark
State the constant of normal distribution.
Answer
View full question & answer→Constants of normal distributions are $\pi $ and $e,$ where $\pi = 3.1416$ and $e = 2.7183$
Question 761 Mark
About which perpendicular line is the normal curve symmetric?
Answer
View full question & answer→The normal curve is symmetric about the perpendicular line $X =\mu .$
Question 771 Mark
What is the area of region bounded by normal curve and $X-$axis$?$
Answer
View full question & answer→The area of region bounded by normal curve and $X-$axis is $1.$
Question 781 Mark
State the parameters of normal distribution.
Answer
View full question & answer→The two parameters of normal distribution are Mean $\mu $ and standard deviation $\sigma .$
Question 791 Mark
State the relationship among the quartiles in normal distribution.
Answer
View full question & answer→In normal distribution two quartiles $Q _1$ and $Q _3$ are equidistant from the second quartile $Q _2= M$. That means $Q_3-M=M-Q_1 \Longrightarrow Q_3+Q_1=2 M$.
Question 801 Mark
Write the symbol for the probability density function of a normal distribution.
Answer
View full question & answer→The probability density function of a normal distribution is denoted by the symbol $f(x).$
Question 811 Mark
The approximate value of mean deviation for a normal distribution is 12. Find its standard deviation.
Answer
View full question & answer→Mean Deviation $\approx 0.8\sigma$
$12 = 0.8\sigma$
$\sigma = \frac{12}{0.8} = 15$.
$12 = 0.8\sigma$
$\sigma = \frac{12}{0.8} = 15$.
Question 821 Mark
"Standard score is independent of unit of measurement". Is this statement true or false ?
Answer
View full question & answer→True. The standard score (Z-score) is a dimensionless value.
Question 831 Mark
The extreme quartiles of normal distribution are 20 and 30. Find its mean.
Answer
View full question & answer→In a normal distribution, the mean is equal to the median. The median is exactly in the center of the extreme quartiles $Q_{1}$ and $Q_{3}$.
$Mean (\mu) = \frac{Q_{1} + Q_{3}}{2} = \frac{20 + 30}{2} = 25$.
$Mean (\mu) = \frac{Q_{1} + Q_{3}}{2} = \frac{20 + 30}{2} = 25$.
Question 841 Mark
What is the skewness of normal distribution ?
Answer
View full question & answer→The skewness of a normal distribution is zero.
Question 851 Mark
What is the shape of normal curve ?
Answer
View full question & answer→The shape of the normal curve is bell-shaped and symmetrical.
Question 861 Mark
Write the function of probability density function for normal variable.
Answer
View full question & answer→$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, where $-\infty < x < \infty$.