The salaries at a corporation are normally distributed with an average salary of $29,000 and a standard deviation of $4,000. What is the probability that an employee will have a salary between $22,520 and $23,480? Enter your answer rounded to exactly 4 decimal places.
Surely you can use the link I gave you when I answered your last post.
Did you even look at it ?
you should get .031177
Teachers’ Salaries in Connecticut The average teacher’s salary in Connecticut (ranked first among states) is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500.
a. What is the probability that a randomly selected teacher makes less than $52,000 per year?
To find the probability that an employee will have a salary between $22,520 and $23,480, we need to calculate the z-scores for each salary and then use the z-table to find the corresponding probabilities.
The z-score formula is:
z = (x - μ) / σ
where:
x = salary
μ = mean (average salary)
σ = standard deviation
For the lower boundary:
z1 = (22,520 - 29,000) / 4,000
And for the upper boundary:
z2 = (23,480 - 29,000) / 4,000
Calculating z1:
z1 = (22,520 - 29,000) / 4,000
z1 = -6,480 / 4,000
z1 = -1.62
Calculating z2:
z2 = (23,480 - 29,000) / 4,000
z2 = -5,520 / 4,000
z2 = -1.38
Now we can look up these z-scores in the z-table to find the corresponding probabilities.
Using the z-table or a statistical calculator, we find that the cumulative probability for z1 of -1.62 is 0.0526, and the cumulative probability for z2 of -1.38 is 0.0838.
To find the probability between these two z-scores, we subtract the lower probability from the higher probability:
Probability = 0.0838 - 0.0526 = 0.0312
Therefore, the probability that an employee will have a salary between $22,520 and $23,480 is approximately 0.0312.