**Average Annual Food Expenditures Away from Home** According to a report by the U.S. Bureau of Labor Statistics, the average annual food expenditures away from home by quintiles of household income before taxes is as follows:| Income Quintile | Lowest 20% | Second 20% | Third 20% | Fourth 20% | Highest 20% ||-------------------------|------------|------------|-----------|------------|-------------|| **Expenditures ($)** | 1036 | 1567 | 2129 | 3208 | 5151 |---Let the random variable X denote a randomly chosen quintile (in income) within the set of all households.**(a) Find the probability distribution associated with these data. (Round your answers to three decimal places.)**| Income Quintile | Lowest 20% | Second 20% | Third 20% | Fourth 20% | Highest 20% ||-------------------------|------------|------------|-----------|------------|-------------|| **Expenditures ($)** | | | | | |**(b) What percentage of the total food expenditures away from home is incurred by the top 40% by income of the population? (Round your answer to three decimal places.)**\[ \text{Percentage:} \quad \_\_\_\_ \% \]**What percentage of the total food expenditures away from home is incurred by the lowest 40% by income of the population? (Round your answer to three decimal places.)**\[ \text{Percentage:} \quad \_\_\_\_ \% \]**Comment on your results.**\[ \text{Comments:} \quad \_\_\_\_\_\_ \]

Given data; Income quintile lowest 20% second 20% third 20% fourth 20% highest 20% expenditures($) 1036 1567 2129 3208 5151 total expenditures($) = 13091let random variable X denotes a randomly chosen quintile (in income) within the set of all households. (a) probability distribution of random variable X; Given data; Income quintile (X) lowest 20% second 20% third 20% fourth 20% highest 20% expenditures($) P(X=x) 103613091=0.079 156713091=0.120 212913091=0.163 320813091=0.245 515113091=0.393 (b) P(top 40%)=P(X=fourth 20%)+P(X=highest 20%)=320813091+515113091=0.639 ANS: 63.9% P(lowest 40%)=P(X=lowest 20%)+P(X=second 20%)=103613091+156713091=0.199 ANS: 19.9%