he monthly incomes of a trainee at a local mill are normally distributed, with a mean of1,100 and a standard deviation of $150. WHAT PERCENTAGE OF THE TRAINEES EARN LESS THAN $800 A MONTH?
800 is two standard deviations below the mean ... a z-score of -2
use a z-score table to find the percentage
To find the percentage of trainees who earn less than $800 a month, we need to calculate the area under the normal distribution curve to the left of the value $800.
First, we need to standardize the value of $800 using the formula:
Z = (X - μ) / σ
Where:
Z is the standardized value (also known as the z-score)
X is the value we want to standardize ($800 in this case)
μ is the mean of the distribution (1,100 in this case)
σ is the standard deviation (150 in this case)
Plugging in the values, we get:
Z = (800 - 1,100) / 150
Z = -300 / 150
Z = -2
Now that we have the z-score, we can find the percentage using a standard normal distribution table or a statistical calculator.
Looking up the z-score of -2 in a standard normal distribution table, we find that the area to the left of -2 is approximately 0.0228 (or 2.28%).
Therefore, approximately 2.28% of the trainees earn less than $800 a month.