20.2% of trainees at the local mill earn less than 880.0 dollars a month.
The incomes of trainees at the local mill are normally distributed with a mean of 1210.0 dollars and a standard deviation of 140.0 dollars. This means that the distribution of incomes follows a normal curve, with most trainees earning close to the mean income of 1210.0 dollars, and fewer trainees earning significantly more or less than the mean.
To find the percentage of trainees earning less than 880.0 dollars a month, we can use the standard normal distribution table (also known as the z-table) to find the proportion of the distribution that is less than 880.0 dollars.
First, we need to convert the income of 880.0 dollars to standard units by subtracting the mean income and dividing by the standard deviation. This gives us (880.0 - 1210.0) / 140.0 = -1.29.
Next, we can look up the proportion of the standard normal distribution that is less than -1.29 on the z-table. This value is approximately 0.202, which means that approximately 20.2% of trainees at the local mill earn less than 880.0 dollars a month.
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