the incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of 150. what percentage of trainees earn less than $900 a month?
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To find the percentage of trainees who earn less than $900 a month, we will use the concept of standard deviation and z-scores.
Step 1: Calculate the z-score for $900.
The z-score formula is given by:
z = (x - μ) / σ
Where:
- x is the value of interest ($900 in this case)
- μ is the mean ($1100 in this case)
- σ is the standard deviation ($150 in this case)
Substituting the values, we have:
z = (900 - 1100) / 150
= -200 / 150
= -1.33
Step 2: Find the corresponding area under the normal distribution curve.
Using a standard normal distribution table or a calculator, we can find the area to the left of the z-score (-1.33). This represents the percentage of trainees earning less than $900.
The table or calculator will give the area as 0.0918 or approximately 9.18%.
Therefore, approximately 9.18% of trainees earn less than $900 a month.