Binomial Random Variable

In a survey of 100 households to determine whether they prefer tea or coffee, define the binomial random variable.

• A type of random variable that can take on any value within a specified range.

• A type of discrete random variable representing the number of households that prefer tea in the survey of 100 households.

• A continuous random variable representing the number of households that prefer tea in the survey of 100 households.

• A random variable that is only defined for a specific interval of values.

In a survey of 100 households to determine whether they prefer tea or coffee, what are the two parameters that define the binomial random variable involved in this study?

• Mean and standard deviation

• Range and interquartile range

• Median and mode

• Number of trials and probability of success

Explain the concept of 'n' in the context of a binomial distribution when analyzing the number of heads in multiple coin flips.

• Number of trials or experiments

• Number of coins flipped

• Probability of success

• Number of successes

In a study observing the success rate of a new medication, what does 'p' represent in the statistical analysis of the binomial random variable?

• standard deviation of the distribution

• probability of success

• mean of the distribution

• number of trials

In the context of STATISTICS, how is the probability mass function (PMF) of a binomial random variable defined when analyzing the likelihood of different outcomes in survey responses?

• The sum of all possible outcomes in a probability distribution

• Probability distribution of the number of specific responses in a fixed number of independent survey questions

• The average of all possible outcomes in a probability distribution

• The median of all possible outcomes in a probability distribution

In a survey of 1000 people, what is the formula for calculating the average number of people who prefer online shopping?

• n^2

• n-p

• n/p

• n*p

Explain the significance of the mean in the context of a statistical survey measuring the frequency of a particular choice among a population.

• The mean represents the highest frequency of a particular choice among the population in the survey.

• The mean represents the average frequency of a particular choice among the population in the survey.

• The mean represents the total population surveyed for a particular choice.

• The mean represents the lowest frequency of a particular choice among the population in the survey.

In a survey of 1000 people, what is the formula for calculating the variance of the number of people who prefer tea over coffee, assuming a binomial distribution?

• n*p^2*(1-p)

• n^2*p*(1-p)

• n*p*(1-p)^2

• n*p*(1-p)

How is the variance used to measure the spread of data in a statistical study?

• Variance only measures the highest data point in a statistical study

• Variance is used to measure the spread of data in a statistical study by providing a measure of how much the data points deviate from the mean.

• Variance is not used to measure the spread of data in a statistical study

• Variance measures the central tendency of data in a statistical study

Provide an example of a real-world scenario where a binomial random variable can be applied in the context of STATISTICS.

• Stock market analysis

• Traffic management

• Weather forecasting

• Quality control in manufacturing