Recent questions tagged probability-and-statistics

A box contains $26$ cards with all English alphabets from $\text{A}$ to $\text{Z}$.The probability of randomly choosing the card with either '$\text{E}$' or '$\text{S}$' ...

Which ONE of the following options is the CORRECT formula for Chi-Square $\left(\chi^{2}\right)$ test?Given, $O_{1}, O_{2}, \ldots . O_{n}$ are the observed values, $E_{1...

Which of the following statements is/are CORRECT in the context of hazardous waste management and its risk assessment?Risk is estimated based on the probability of an act...

A $6$-hour rainfall of $6$ cm at a station was found to have a return period of $40$ years.The probability that a $6$ -hour rainfall of this or larger magnitude will occu...

Standard deviation for the particulate matter (PM) concentrations listed in the table is $\_\_\_\_$ $\mu \mathrm{g} / \mathrm{m}^{3}$ (rounded off to one decimal place).$...

​The number of patients per shift $(X)$ consulting Dr. Gita in her past $100$ shifts is shown in the figure. If the amount she earns is ₹ $1000(X-0.2)$, what is the avera...

​​​​​Consider the following statements$P$: According to the National Ambient Air Quality Standards (Central Pollution Control Board, Govt. of India, notification $2009$),...

​​​​​​Consider the following statementsEnvironmental pollutant concentration is generally modeled using lognormal distribution.Environmental pollutant concentration is ge...

A residential family is considering two cities for relocation. The data related to pollutant exposure and associated health cost per year are given in the following figur...

An industry releases three greenhouse gases $\mathrm{(GHGs)}$, $\mathrm{CO}_{2}(5 \mathrm{~kg} /$ day $), \mathrm{CH}_{4}(0.5$ $\mathrm{kg} /$ day $)$, and $\mathrm{N}_{2...

Water from a hand pump located near a landfill has $1 \mathrm{mg} / \mathrm{L}$ arsenic (oral carcinogenic potency factor $=1.75(\mathrm{~kg-day}) / \mathrm{mg})$. A pers...

The probability of a boy or a girl being born is $1 / 2$. For a family having only three children, what is the probability of having two girls and one boy?$3 / 8$$1 / 8$$...

Ten cards in a pack are numbered as $1,2,3, \ldots 10$. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is$4 / 10...

A population $\text{(with mean $\mu$)}$ follows normal distribution. Ten samples $(N)$ are drawn at random with a mean value of " $x$ " and standard deviation of " $S$ "....

Given a fair six-faced dice where the faces are labelled $'1'$, $'2'$, $'3'$, $'4'$, $'5'$, and $'6'$, what is the probability of getting a $'1'$ on the first roll of the...

A recent survey shows that $65 \%$ of tobacco users were advised to stop consuming tobacco. The survey also shows that $3$ out of $10$ tobacco users attempted to stop us...

A researcher compiled the following information about the performance of a kit in an outbreakInfection stateKit responseDisease (probability =0.002)Positive response (pro...

$\text{W1, W2, W3...W9}$ represent the holding times of $9$ water samples, which follow a normal distribution with mean $=8.33$ and standard deviation $=4.472$.$\text{M}$...

An industry with an effective stack height of $80 \mathrm{~m}$ emits $1200 \mathrm{~g} / \mathrm{h}$ of $\mathrm{CO}$. The windrose plotted using the meteorological data ...

Ultimate analysis of a municipal solid waste sample is given below\begin{array}{|c|c|c|c|c|}\hline { Percent by weight } \\\hline Carbon & Hydrogen & Oxygen & Nitrogen & ...