The average teachers salary in Connecticut( ranked first among states) is $57,337. suppose that the distribution of salaries is normal with a standard deviation of $7500.
What is the probability that a randomaly selected teacher makes less than $52,000 per year?
0.2389
0.2389
To find the probability that a randomly selected teacher makes less than $52,000 per year, we need to use the standard normal distribution.
First, we need to standardize the value using the formula:
z = (x - μ) / σ
where:
- x is the value we want to standardize ($52,000 in this case)
- μ is the mean of the distribution ($57,337)
- σ is the standard deviation of the distribution ($7,500)
Substituting the values into the formula:
z = (52,000 - 57,337) / 7,500
= -0.7083
Next, we need to find the probability corresponding to this standardized value from the standard normal distribution table or using a calculator.
Using the standard normal distribution table, we can look up the cumulative probability for z = -0.7083. The table will give us the area under the standard normal curve to the left of this z-value.
The cumulative probability is approximately 0.2396.
Therefore, the probability that a randomly selected teacher makes less than $52,000 per year is approximately 0.2396 or 23.96%.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.