Using Excel To Generate Probability Distribution For A Binomial Random Variable And Analyzing Data On Household Size And Computer Usage In The US

Use Excel to generate the probability distribution for a binomial random variable for which there are 1000 trials (n = 1000) and the probability of success is 0.7 (p = 0.7).

The 2010 U.S. Census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of persons living in each was reported as follows.

 2       3        1        2         6         4         2        1        5        3         2        3        1        2         2      1       3        1       2       2       4        2         1         2          8            3           2          1         1        3

1. Calculate the mean and median. What information do you obtain from these two values Does one seem more appropriate than the other for this sample
2. Calculate the variance and standard deviation. What do these statistics reveal

According to the Consumer Electronics Manufacturers Association, 10% of all U.S. households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S. households having a fax machine have a personal computer. A U.S. household is randomly selected.

1. What is the probability that the household has a fax machine and a personal computer
2. What is the probability that the household has a fax machine or a personal computer
3. What is the probability that the household has a fax machine and does not have a personal computer
4. What is the probability that the household has neither a fax machine nor a personal computer.

• Mean and median

Mean = sum of data points/ sample size (n) = 75/30 = 2.50

Median

Sort the data in ascending order

Sample size = 30 (even number)

The mean and median are representative of the central tendency of the given data and highlights the average number of people in a household. Considering that the data may contain outliers in the form of household with 6 and 8 members, it would be appropriate to use median instead of mean as the mean may be influenced by extreme values which is not the  case for median.

• Variance and standard deviation

Standard deviation  

The above statistics reveal the dispersion in the data and the deviation of the data points from the average value.

Percentage of US households has fax machine = 10%

Percentage of US households has personal computer= 52%

Percentage of US households has fax machine and has personal computer P(PC| Fax) =91%

Joint probability table can be formed based on the above shown probabilities

• Probability that a randomly selected US household would has a fax machine and a personal computer 

• Probability that a randomly selected US household would has a fax machine or a personal computer

• Probability that a randomly selected US household would has a fax machine and does not have a personal computer

• Probability that a randomly selected US household would has neither a fax machine nor a personal computer.