Question

It is known that the distribution of income is right skewed with a mean of $50,000 per week and a standard deviation of $7000. If a random sample of 400 citizens is taken, what is the distribution of the average income level?

Select one:
a. Left skewed with mean $50,000 and standard deviation $350.
b. Right skewed with mean $50,000 and standard deviation $350.
c. Right skewed with mean $50,000 and standard deviation $7000.
d. Normal with mean $50,000 and standard deviation $7000.
e. Normal with mean $50,000 and standard deviation $350.

Answer 1

The distribution of the average income level is normal with a mean of $50,000 and a standard deviation of $350. The standard deviation can be greater than the average in a right-skewed distribution. It is more likely for the average salary of the 1,000 residents to be from $2,000 to $2,100 rather than from $2,100 to $2,200. The correct answer for the distribution of the average income level is therefore 'e. Normal with mean $50,000 and standard deviation $350.'

Step-by-step explanation:

The distribution of the average income level is normal with a mean of $50,000 and a standard deviation of $350.

To understand why the standard deviation can be greater than the average, it is important to note that the standard deviation measures the spread or variability of the data, while the average represents the central tendency. In a right-skewed distribution, there are a few extreme high values that can greatly affect the spread of the data.

It is more likely for the average salary of the 1,000 residents to be from $2,000 to $2,100 than from $2,100 to $2,200 because the majority of the salaries are closer to the $2,000 mark. Since the distribution is right-skewed, there are relatively fewer incomes in the higher range, making it less likely for the average to move into that range.