Final answer:
To find the cutoff salary for teachers in the bottom 10%, you need to calculate the z-score using the mean and standard deviation. Then, use the z-score to find the cutoff salary by rearranging the formula.
Step-by-step explanation:
To find the cutoff salary for teachers in the bottom 10%, we need to calculate the z-score.
The formula for calculating the z-score is: z = (X - μ) / σ
Where X is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, we want to find the cutoff salary, so X will be the salary we are looking for. μ is the mean of $37,000 and σ is the standard deviation of $5000.
Now, we can use a standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 10% (0.1).
Once we have the z-score, we can use it to find the cutoff salary by rearranging the formula: X = (z * σ) + μ
Substituting in the values, we can calculate the cutoff salary.