4 Marks Each

Question 14 Marks

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 $?$

Answer

$(1)\ 4.17$ hours $(2)\ 1789$

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Question 24 Marks

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.

Answer

Mean $=₹\ 20$, Standard deviation $=₹\ 3$

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Question 34 Marks

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 $₹ 30,000\ ?$

Answer

$(1)\ ₹ 32,000\ (2)\ 20$ days

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Question 44 Marks

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?

Answer

$71.3$ inch, $1.88 \%$

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Question 54 Marks

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 $?$

Answer

$(1)\ 121\ (2)\ 54.08$ days

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Question 64 Marks

The weekly demand of tube-lights of Delta Electricals in a shop follows normal distribution with mean $100 .$ It is found that $90 \%$ times the weekly demand of tube-lights is less than $115 .$
$(1)$ Find the standard deviation of weekly demand of tube-lights.
$(2)$ If a stock of $120$ tube-lights is kept in the shop every week,find the probability that the stock would be insufficient.

Answer

$(1)\ 11.72\ (2)\ 0.0436$

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Question 74 Marks

The probability density function of a variable $X$ is as follows. $ f(x)=\frac{1}{\sqrt{3200 \pi}} e^{-\frac{(x-120)^2}{3200}}, -\infty$

Answer

$(1)\ 0.4649 \ (2)\ 90$

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Question 84 Marks

The probability density function of a normal variable $X$ is given below. $ f(x)=k \cdot e^{-\frac{1}{8}(x-12)^2}\ (1)$ Find the value of $k.\ (2)$ Find the variance of the variable. $(3)$ Find the extreme quartiles of the variable.

Answer

$(1)\ \frac{1}{2 \sqrt{2 \pi}}$
$(2)\ 4$
$(3)\ Q_1=10.65, Q_3=13.35$

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Statistics 4 Marks Each

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