Sample QuestionsPART 2 : NORMAL DISTRIBUTION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $P(-\infty)$
- A
$z_1=0$
- ✓
$z_1<0$
- C
$z_1>0$
- D
$z_1=1$
Answer: B.
View full solution →The mean and standard deviation of a normal variable $X$ are $20.5$ and $5$ respectively. Find $P(0 \leq x \leq 26.5)$.
- A
$0.1151$
- B
$0.8849$
- ✓
$0.3849$
- D
$0.7698$
Answer: C.
View full solution →If $P\left(0 \leq z \leq z_1\right)=0.377$ for the standard normal variable $Z$, state the value of $P (-\infty)$
- ✓
$0.123$
- B
$0.877$
- C
$0.754$
- D
$0.377$
Answer: A.
View full solution →What will be the value of $P(-\infty)$
- A
$0.3413$
- B
$0.1915$
- C
$0.4772$
- ✓
$0.5$
Answer: D.
View full solution →What will be the value of $P(z=1.5)$ for the standard normal variable $Z$ ?
- A
$0.4332$
- B
$0.9332$
- ✓
$0$
- D
$0.0668$
Answer: C.
View full solution →If the value of $z-$ score for $x=174$ is $1.2$, find the mean of the variable.
View full solution →The standard deviation of a normal variable $X$ is $20 .$
View full solution →Find the area under the normal curve to the left of a perpendicular at $z=1.75$ for a standard normal variable.
View full solution →The mean of normal variable is $125$ and the standard deviation is $17.$ Obtain the range of central $99 \%$ observations of this variable.
View full solution →What percentage of observations of a normal variable are less than $\mu+1.96 \sigma$ ?
View full solution →The normal distribution of marks of a group of students is $N(40,64)$. Find the probability that the marks of a student of this group will be more than $36 .$
View full solution →The average monthly salary of workers in a factory is $₹ 7,000$ and its standard deviation is $₹ 400$. If the distribution of monthly salary of workers is normal, find the probability that a worker in this factory earns less than $₹ 8,000$.
View full solution →If $P\left(-1 \leq z \leq z_1\right)=0.823$ for a $z$ - score $z_1$ of the standard normal variable, find the value of $z_1$.
View full solution →If $P\left(1.1 \leq z \leq z_1\right)=0.125$ for the standard normal variable $Z$, find the value of $z_1$.
View full solution →Find the value of $P(|z| \leq 1.25)$ for the standard normal variable $Z$.
View full solution →if the mean of a normal distribution is $20$ and the mean deviation is $12,$ find its extreme quartiles.
View full solution →The marks in Statistics of students studying in a class follows normal distribution. The mean of this distribution is $65$ marks and standard deviation is $5$ marks. If $10$ students have scored less than $60$ marks, estimate the total number of students.
View full solution →According to the survey of a company manufacturing school uniforms, the average waist size of students of a school is $66 cm$ and its standard deviation is $5\ cm$. What will be the percentage of students having waist size $(1)$ more than $72\ cm ?\ (2)$ less than $62 cm$ ? $($Use normal distribution.$)$
View full solution →The mean and standard deviation of a normal variable are $52$ and $8$ respectively. Find the fourth decile and interpret it.
View full solution →The monthly personal expense of $500$ students residing in a $(₹ 500$. If the monthly expense follows normal distribution, how many students will have monthly expense$)\ (1 )$ between $₹\ 4300$ and $₹\ 6100\ ?\ (2)$ more than $₹\ (5200) ?$
View full solution →The time taken by participants to complete the run in a
full marathon race follows normal distribution with
mean $5$ hours and standard deviation $0.8$ hours.
$(1)$ What will be the maximum time in the fastest running
$15 \%$ participants $?$
$(2)$ Out of $2000$ participants, how many would complete
their run in $6$ hours $?$
View full solution →The distribution of expenses on food items from canteen
of students of a school is normal. $50 \%$ students
spend more than $₹\ 20$ daily, whereas the probability of
any student spending more than $₹\ 26$ is $0.0228$. Find
the mean and standard deviation of expenses by students
on food items.
View full solution →According to the sales report of a company, the standard
deviation of daily sales is $₹ 5000.$ Sales follow normal
distribution.
$(1)$ If the sales of company is less than $₹ 24,625$ in $7 \%$
cases, find the mean sales.
$(2)$ Approximately how many days in a month will the
sales be more than $₹ 30,000\ ?$
View full solution →The heights of doors of a building is to be decided in such a way that $99 \%$ persons who will reside there would not require to bend while passing through it. If the height of persons living in that area follows normal distribution with mean and standard deviation $62$ inches and $4$ inches respectively, what should be height of the door ? If the height of the door is kept I inch less than your answer, what percentage of people will have to bend to pass through the door?
View full solution →On an average $44$ days are required to complete an online course of a university and its standard deviation is $12$ days.Assume that the time taken for completing this course follows normal distribution. If $1000$ students have registered for this course,
$(1)$ how many of them would complete this course with in $30$ days$?$
$(2)$ in how many days would 800 students complete the course $?$
View full solution →The result of an examination is as follows:
| Result |
No. of students |
| Pass with distinction |
$500$ |
| Pass without distinction |
$3000$ |
| Fail |
$1500$ |
| Total |
$5000$ |
Minimum $40$ marks out of $100$ are necessary to pass this examination and at least $70$ marks are needed to get distinction. If the marks of examination follows normal distribution, find the mean and standard deviation of the distribution. View full solution →$5 \%$ persons of a large group have heights less than $132 \ cm$ and $40 \%$ persons have height between $132 \ cm$ and $143 \ cm$. Assuming that the distributio of height of these persons is normal, find the mean and standard deviation of their height.
View full solution →The standard deviation of monthly salaries of a group of $150$ employees is $₹ 750 .$ The distribution of monthly salary is normal. If the probability of an employee having salary less than $₹ 11,125$ is $0.9332$, how many employees would have salary between $₹ 9,250$ and $₹ 11,500 ?$
View full solution →The average production of a certain grain in plots of one
acre in a taluka is $2000\ kg$ and the variance is $8100( kg )^2$. The production of grains follows normal distribution.
$(1)$ What is the minimum production in the $20 \%$ plots having maximum production ?
$(2)$ What percent of plots will have the production between $1950\ kg$ and $2150\ kg$ ?
View full solution →The diameter of copper wire follows normal distribution.
If the mean of its normal distribution is $11\ mm$ and
standard deviation is $1\ mm$, find $P _{15}$ and
$(D _9)$ of the distribution and interpret them.
View full solution →