Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $36,000 and a standards deviation of $6000. What is the cutoff salary for teachers in the bottom 10%?
Answer choice:
a. $28,320
b. $43,680
c. $45,870
d. $26,130
What is your thinking? http://davidmlane.com/hyperstat/z_table.html
Nice
http://www.jiskha.com/display.cgi?id=1271428581
ok I got b for the answer is that correct?
If it is for the bottom 10% it must be lower than the mean!
ok so it will be a?
To find the cutoff salary for teachers in the bottom 10%, we need to determine the salary value that corresponds to the 10th percentile of the normal distribution.
First, we calculate the z-score corresponding to the 10th percentile. The z-score tells us how many standard deviations the salary is from the mean. We can use a standard normal distribution table or a calculator to find this value.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
x = cutoff salary
μ = mean salary
σ = standard deviation
Substituting the given values into the formula:
z = (x - $36,000) / $6,000
Looking up the z-score for a cumulative area of 0.10 in a standard normal distribution table, we find that the z-score is approximately -1.282.
Now, solving for x in the z-score formula and substituting the known values:
-1.282 = (x - $36,000) / $6,000
Multiply both sides by $6,000:
-1.282 * $6,000 = x - $36,000
Simplifying the equation:
-$7,692 = x - $36,000
Adding $36,000 to both sides:
x = $36,000 - $7,692
x = $28,308
Therefore, the cutoff salary for teachers in the bottom 10% is approximately $28,308.
The closest answer choice to $28,308 is option (a) $28,320.