Sample QuestionsNORMAL DISTRIBUTION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the distribution of normal variable is shown as $N(20,4)$ then which of the following intrvals includes $99.73\%$ of observations$ ?$
- A
$(18, 22)$
- B
$(16, 24)$
- ✓
$(14, 26)$
- D
$(12, 28)$
Answer: C.
View full solution →For a normal distribution, approximate value of mean deviation is $20.$ Which of the following is the value of quartile deviation ?
- A
$\frac{25}{3}$
- B
$\frac{32}{3}$
- C
$24$
- ✓
$\frac{50}{3}$
Answer: D.
View full solution →Which of the following is approximate value of quartile deviation for standard normal variable ?
- A
$\frac{2}{3}\sigma$
- ✓
$\frac{2}{3}$
- C
$\frac{4}{5}\sigma$
- D
$\frac{4}{5}$
Answer: B.
View full solution →Normal distribution is a probability distribution of which type of random variable?
- A
- ✓
Continuous random variable
- C
- D
Answer: B.
View full solution →State the symbol for the probability density function of normal distribution.
- A
$P (x)$
- B
$R (x)$
- ✓
$F(X)$
- D
$F(Z)$
Answer: C.
View full solution →Mean of a normal distribution is $13.25$ and its standard deviation is $10.$ Estimate the value of its third quartile.
View full solution →What percentage of area is covered under the normal curve within the range $\mu-2 \sigma$ to $\mu+2 \sigma ?$
View full solution →Which value of normal variable divides the area of normal curve in two equal parts?
For which value of standard normal variable, the standard normal curve is symmetric on both the sides?
“Standard score is independent of unit of measurement”, Is this statement true or false?
A normal variable $X$ has following probability density function: $f(x)=\frac{1}{\sqrt{5000 \pi}} e^{-\frac{1}{5000}(x-75)^{2}},-\infty \leq x \leq \infty$ From this, answer the following questions: $(1)$ If $P \left[60 \leq X \leq x_{2}\right]=0.5670$, then find $x_{2}$. $(2)$ If $P \left[x_{1} \leq X \leq 125\right]=0.3979$, then fmd $x_{1}$. $(3)$ Find $P[\mid X-50 I \leq 10]$
View full solution →For a normal variable, mean deviation is $48$ and its third quartile is $120.$ Estimate its first quartile.
View full solution →The extreme quartile of a normal variable are $10$ and $30.$ Find its mean deviation.
View full solution →A normal variable $X$ has the probability density function as, $f(x)=$ constant $\times e^{-\frac{1}{50}(x-10)^2} ;-\infty$
View full solution →Define standard normal variable and write its probability density function.
If the probability that value of standard normal variable $Z$ lies between 0 and $Z$-score $\left(z_{1}\right)$ is $0.3925$ then obtain the possible values of $Z$-score $\left(z_{1}\right)$.
View full solution →The number of vehicles arriving at toll station during busy hours of national highway follows normal distribution. The mean of this distribution is ,u and its standard deviation is $0'.$ The number of vehicles arriving at two different busy time periods are $88$ and $64$ and if the respective values of $Z-$score for these values are $0.8$ and $-0.4$ then find mean and standard deviation of number of vehicles arriving at the toll station during busy period.
View full solution →For a normal distribution, the first quartile and the mean deviation are $20$ and $24$ respectively. Obtain an estimate of the value of mode.
View full solution →The extreme quartiles for a normal distribution are $20$ and $50$ respectively. Obtain the limits which include $95\%$ of the observations of the distribution.
View full solution →The probability density function of a normal variable $X$ is defined as under $ f(x)=\text { constant } \cdot e^{-\frac{1}{2}\left(\frac{x-25}{10}\right)^{2}}; -∞ < x < ∞ $ From this normal distribution estimate the values of the following : $(1)$ Third quartile $(2)$ Quartile deviation $(3)$ Mean deviation
View full solution →If the probabilities for standard normal variable $Z$ are as under then obtain the value of $Z$-score $\left(z_{1}\right) : (1)$ Area to the left of $Z=z_{1}$ is $0.10$. $(2)$ Area to the right of $Z=z_{1}$ is $0.90$.
View full solution →If the probabilities for standard normal variable $Z$ are as under then obtain the value of $Z$-socre $\left(z_{1}\right)$ :
$(1)$ Area to the left of $Z=z_{1}$ is $0.95$
$(2)$ Area to the right of $Z=z_{1}$ is $0.05$.
View full solution →The monthly income of workers working in a production house follows normal distribution. Their average monthly income is ? $15,000$ and standard deviation is $4000.\ (1)$ If a worker is selected at random then find the probability that his monthly income is between $₹ 10,000$ and $₹ 25,000.\ (2)$ Find the percentage of workers having monthly income between $₹ 12,000$ and $₹ 22,000$ in the production house.
View full solution →The average weight of grown up children living in a large society is $50 \ kg$ and its standard deviation is $5 \ kg.$ If their weight follows normal distribution and a grown up child is selected at random then find $(1)$ the probability that his weight is between $55 \ kg$ and $65 \ kg.\ (2)$ the probability that his weight is between $35 \ kg$ and $45 \ kg.$
View full solution →The number of students in classes of higher secondary schools of a city follows normal distribution. Average number of students in the classes is $50$ and standard deviation is $15.$ If a class is selected at random then find the following probabilities $(i)$ a class consists of more than $68$ students $(ii)$ a class consists of less than $32$ students.
View full solution →If $Z$ is standard normal variable and $z_{1}$ is $Z$-score then obtain the values of $z_{1}$ satisfying the following conditions
$(1) P\left(-1 \leq Z \leq z_{1}\right)=0.5255$
$(2) P\left(z_{1} \leq Z \leq 2\right)=0.7585$
View full solution →The probability density function of a normal variable is as under $ f(x)=\frac{1}{4 \sqrt{2 \pi}} \quad e^{-\frac{1}{32}(x-50)^{2}} ; \quad-\infty < x < \infty $ Obtain parameters of this distribution and find the values of following : $(1) P(52 \leq X \leq 58) \ (2)\ P(|X-45| \leq 4)$
View full solution →The maximum temperature of a city during summer follows normal distribution. On a particular day, the probability that the maximum temperature of the city is more than $31^\circ $ Celsius is $0.3085,$ whereas the probability that during some other day, the maximum temperature is less than $2?^\circ $ is $0.0668.$ Find mean and standard deviation of the maximum temperature of the city.
View full solution →The monthly income of a group of employees follows normal distribution. The mean of the distribution is $₹ 15,000$ and its standard deviation is $₹ 4000 .$ From this information, $(1)$ obtain range of monthly income for middle $60 \%$ of the employees. $(2)$ if monthly income of $250$ employees is between $₹ 15000$ apd certain fixed income $₹ x_{1}$ then find the value of $x_{1}$.
View full solution →$200$ students are selected from all the students of a school and the marks obtained by them in an examination of $100$ marks follows normal distribution. The mean marks of the distribution is $60$ and its standard deviation is $8.$
$(1)$ If $70$ or more marks are required for the special scholarship then obtain the number of students getting special scholarship.
$(2)$ Obtain the minimum marks of $10\%$ of the students getting maximum marks. Here, $X =$ marks obtained by a student
View full solution →