Mathematics

Probability Distributions

488 Questions

Probability distributions describe the likelihood of different outcomes in a statistical experiment. Key topics include calculating confidence intervals, understanding Type II errors, and working with the standard normal distribution. These concepts are frequently tested in mathematics and statistics sections of various competitive exams.

Standard normal distributionType II error probabilityConfidence interval interpretationPoisson distributionProbability density function

Probability Distributions Questions

Multiple choice business economics and quantitative methods measures of dispersion and skewness quartile deviation or semi-interquartile range interquartile range histograms and frequency distribution diagrams

The $P _82$ for the following distribution is

X 2 3 4 5 6 7 8 9 10 11
Y 3 6 9 18 20 14 10 10 7 2


  1. $6$
  2. $5$
  3. $8$
  4. $9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total frequency N = 99. The 82nd percentile position is 0.82 * (99 + 1) = 82nd value. Looking at the cumulative frequencies (3, 9, 18, 36, 56, 70, 80, 90, 97, 99), the 82nd value falls within the category X = 9.

Multiple choice zoology menustral cycle in human parturition and lactation pregnancy and birth fertilization and post fertilization in humans

If a couple has four girls ,the probability of fifth child being male is _________.

  1. $50\%$
  2. $25\%$
  3. $75\%$
  4. $100\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The gender of the consecutive children does not depend on each other. So, every time the couple has a kid, there is equal chances of them having a girl or a boy. Therefore, the probability would be 50% reasonably. 

Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

If the chance that a vessel arrives safely at a port is $\dfrac 9{10}$ then what is the chance that out of $5$ vessels expected at least $4$ will arrive safely?

  1. $\dfrac {14 \times 9^4}{10^5}$
  2. $\dfrac {15 \times 9^5}{10^4}$
  3. $\dfrac {14 \times 9^3}{10^4}$
  4. $\dfrac {14 \times 9^6}{10^5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a binomial distribution problem where n=5, p=0.9, q=0.1. P(X>=4) = P(X=4) + P(X=5). P(X=4) = 5C4 * (0.9)^4 * (0.1)^1 = 5 * 0.9^4 * 0.1 = 0.5 * 9^4 / 10^4 = 5 * 9^4 / 10^5. P(X=5) = 5C5 * (0.9)^5 = 9^5 / 10^5. Sum = (5 * 9^4 + 9 * 9^4) / 10^5 = 14 * 9^4 / 10^5.

Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

A box contains nine bulbs out of which $4$ are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective.

  1. $\dfrac{62}{63}$
  2. $\dfrac{125}{126}$
  3. $\dfrac{1}{63}$
  4. $\dfrac{1}{126}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total number of ways to choose 4 bulbs from 9 is 9C4 = 126. The number of ways to choose 4 defective bulbs from the 4 available is 4C4 = 1. Thus, the probability is 1/126.

Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

The probability that A speaks truth is $\dfrac35$ and that of B speaking truth is $\dfrac47$. What is the probability that they agree in stating the same fact?

  1. $\dfrac {18}{35}$
  2. $\dfrac {12}{35}$
  3. $\dfrac {17}{35}$
  4. $\dfrac {19}{35}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

They agree if both tell the truth or both lie. P(Both Truth) = (3/5)(4/7) = 12/35. P(Both Lie) = (2/5)(3/7) = 6/35. Total probability = 12/35 + 6/35 = 18/35.

Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

The probability of success of three students X,Y and Z in the one examination are $\dfrac15, \dfrac14$ and $\dfrac13$ respectively. Find the probability of success of at least two.

  1. $\dfrac16$
  2. $\dfrac25$
  3. $\dfrac34$
  4. $\dfrac35$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probabilities of success: P(X)=1/5, P(Y)=1/4, P(Z)=1/3. P(Failures): P(X')=4/5, P(Y')=3/4, P(Z')=2/3. At least two success = P(exactly 2) + P(exactly 3). P(exactly 3) = (1/5)(1/4)(1/3) = 1/60. P(exactly 2) = (1/5)(1/4)(2/3) + (1/5)(3/4)(1/3) + (4/5)(1/4)(1/3) = 2/60 + 3/60 + 4/60 = 9/60. Total = 10/60 = 1/6.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Probability can take values from ______.

  1. -3 to 3

  2. -3 to 1

  3. 0 to 1

  4. -1 to 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1. 
Multiple choice business economics and quantitative methods nature and scope of economics definition, scope, importance and limitation of statistics introduction - statistics for economics meaning and definition of statistics

Range of probability distribution with 68.26% lies within __________________.

  1. $(+ 3 \sigma$ and $-3\sigma )$
  2. $(+ 4 \sigma$ and $-4\sigma )$
  3. $(+ 1 \sigma$ and $-1\sigma )$
  4. $(+ 2 \sigma$ and $-2\sigma )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a normal distribution, approximately 68.26% of the data falls within one standard deviation (sigma) of the mean, which is represented as the range between -1 sigma and +1 sigma.

Multiple choice business economics and quantitative methods nature and scope of economics definition, scope, importance and limitation of statistics introduction - statistics for economics meaning and definition of statistics

____ provides the basis of theory of probability in statistics.

  1. Law of inertia of large numbers

  2. Law of statistical regularity

  3. Law of averages

  4. Both A and B
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statistical regularity is a law in statistics that states that random events will exhibit similar properties when repeated enough times, that it they will follow a regular pattern. All central limit theorems and low of large numbers are laws of statistical regularity.