statistics

The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed wi...

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), P(x), of a variable x?

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Furt...

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Furt...

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?

A set of observations of independent variable ($x$) and the corresponding dependent variable ($y$) is given below. | $x$ | 5 | 2 | 4 | 3 | |---|---|---|---|---| | $y$ | 16 | 10 | 1...

A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below. x 5 2 4 3 y 16 10 13 12 Based on the data, the coefficient a of the l...

The frequency distribution of the compressive strength of 20 concrete cube specimens is given in the table. If μ is the mean strength of the specimens and σ is the standard deviati...

For the function f(x)=a+bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?

The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the va...

Type $${\rm I}{\rm I}$$ error in hypothesis testing is

The spot speeds (expressed in km/hr) observed at a road section are $$66, 62, 45, 79, 32, 51, 56, 60, 53$$ and $$49.$$ The median speed (expressed in km/hr) is __________.

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Pois...

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The probability that the annual precipi...

If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$33$$ kmph, the coefficient of variation in speed is