Final answer:
C) $600By substituting the values—mean, standard deviation, and z-score—into this formula, the estimate for the highest weekly wages of the 300 lowest-paid workers in the factory area is $600.
Explanation:
The estimate for the highest weekly wages of the 300 lowest-paid workers can be determined using the z-table and the cumulative probability. Since the data follows a normal distribution, about 15% of the values lie below one standard deviation from the mean, leaving 85% of values above. By finding the z-score for the 15th percentile (which is approximately -1), we can calculate the corresponding wage using the formula: estimated wage = mean + (z-score * standard deviation). With a z-score of -1, assuming a standard deviation of $200, the calculation results in $600.
In a normally distributed dataset, the mean lies at the center, with standard deviations showing the spread of data. The z-score represents the number of standard deviations a particular value is from the mean. By using the z-table or statistical software, one can determine the percentile associated with a specific z-score. In this case, finding the z-score for the 15th percentile indicates that 15% of the data lies below that value. Therefore, for the 300 lowest-paid workers (15% of the total), the estimate can be made based on this percentile, which corresponds to a z-score of approximately -1.
The formula to estimate the wage using the z-score involves adding or subtracting the product of the z-score and the standard deviation to or from the mean. By substituting the values—mean, standard deviation, and z-score—into this formula, the estimate for the highest weekly wages of the 300 lowest-paid workers in the factory area is $600.