Final answer:
In a bell-shaped distribution, we can estimate the percentage of salaries that are less than $80,000 or more than $104,000 using the z-score. The z-score for $80,000 is -2, which indicates that approximately 2.28% of salaries are less than $80,000. The z-score for $104,000 is 2, indicating that approximately 2.28% of salaries are more than $104,000.
Step-by-step explanation:
In a bell-shaped distribution, which is also known as a normal distribution, the percentage of salaries that are less than $80,000 or more than $104,000 can be estimated using the z-score. The z-score measures the number of standard deviations a specific value is from the mean. To calculate the z-score for $80,000 and $104,000, we can use the formula:
z = (x - mean) / standard deviation
Using the given mean of $92,000 and standard deviation of $6,000, we can calculate the z-score for $80,000:
z = (80,000 - 92,000) / 6,000 = -2
Similarly, the z-score for $104,000 can be calculated:
z = (104,000 - 92,000) / 6,000 = 2
The percentage of salaries that are less than $80,000 can be found by finding the area under the normal distribution curve to the left of the z-score.
From a standard normal distribution table or a statistical calculator, we can find that the area to the left of -2 is approximately 0.0228 or 2.28%. So, approximately 2.28% of salaries are less than $80,000.
The percentage of salaries that are more than $104,000 can be found by finding the area under the normal distribution curve to the right of the z-score.
With the same methods, we can find that the area to the right of 2 is approximately 0.0228 or 2.28%. So, approximately 2.28% of salaries are more than $104,000.