Question

Assume that Thailand's government reports its population mean disposable
household income is $900 per month, with a standard deviation of $100. Indonesia's population mean is $1,000, with a standard deviation of $300.

a. Which country has more variation in income? Explain using popular phrases,
such as “gap between rich and poor.”

b. Each country defines the poverty level to be $750. If you assume that income
has a normal distribution, find the probability that a household’s income is below
the poverty level in

i. Thailand

ii.Indonesia

c. Based on answer b, Does it seem reasonable to assume a normal distribution? Is income symmetric
or skewed?

Answer 1

Part a

Here, we have to use the coefficient of variations for the comparison of variation in incomes in two countries Thailand and Indonesia.

Coefficient of variation = CV = SD / Mean

For Thailand, mean and standard deviation for income ($) are given as below:

Mean = 900, SD = 100

CV = 100/900 = 1/9 = 0.11 or 11%

For Indonesia, mean and standard deviation for income ($) are given as below:

Mean = 1000, SD = 300

CV = 300/1000 = 3/10 = 0.30 or 30%

CV of Indonesia is 30% and CV for Thailand is 11%. This means Indonesia have more variation in income than Thailand.

This means, there is more gap between the rich and poor people in Indonesia as compared to Thailand.

Part b

Here, we have to find P(X<750) for both countries.

Z = (X – mean)/SD

i) Thailand

Mean = 900, SD = 100

Z = (750 – 900) / 100

Z = -1.5

P(Z< -1.5) = 0.066807201 (by using z-table or excel)

Required Probability = 0.066807201

ii) Indonesia

Mean = 1000, SD = 300

Z = (750 – 1000) / 300

Z = -0.833333333

P(Z< -0.833333333) = 0.202328381 (by using z-table or excel)

Required probability = 0.202328381

Part c

It does not seem reasonable to assume a normal distribution because there is a significant difference between the above two probabilities. Also, distribution of income is skewed because there are two different tail probabilities for the same poverty level of $750.