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The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country with a wedge shaped distribution. Let the average salary be $2,000 per year with a standard deviation of $6,000. We randomly survey 1,000 residents of that country. (a) In words, define the random variable X. O the number of people surveyed O the yearly income of someone in a Third World country O the number of people who have a salary of $2,000 per year O the yearly income for each person in a Third World country (b) In words, define the random variable X. O the average salary of all residents in a Third World country O the average salary from a sample of 1,000 people throughout the world O the average salary from a sample of 1,000 residents of a Third World country the average salary of all residents in the world (c) Give the distribution of X. (Round your numerical values to two decimal places.) XN ? (d) How is it possible for the standard deviation to be greater than the average? This is an example of a poor survey; the average should never be smaller than the standard deviation. O Very wide differences in data values can have averages smaller than standard deviations. O Very small differences in data values can have averages smaller than standard deviations. (e) Why is it more likely that the average of the 1,000 residents will be from $2,000 to $2,100 than from $2,100 to $2,200? The sample size was sufficiently large to ensure a sample mean close to the population mean. Because the standard deviation is so high, there is a high probability the sample mean is close to the population mean. O The distribution of the sample mean will have higher probabilities closer to the population mean. O It is actually more likely that the average of the 1,000 residents will be from $2,100 to $2,200