A company has been studying the performance of their sales department. The measure of performance used is: average monthly sales amount in dollars. For the past 12 months, the average monthly sales amount has been $4,532 with a standard deviation of $386. Calculate the percentage of months that the average monthly sales amount exceeds $5,800.
== here is what I have is this correct?
== P(X>5800)=1-P(Z<(5800-4532)/386)=1-P(Z<3.285)=1-0.99949=0.00051
== how do I get the number of monthly sales that exceed. I feel like I haven't finished the problem.
To calculate the percentage of months in which the average monthly sales amount exceeds $5,800, you have already taken the first step correctly by converting the data to z-scores. However, you need to use the cumulative probability function based on the z-score to find the desired percentage.
Here's a step-by-step explanation of how to calculate it:
1. Calculate the z-score:
z = (value - average) / standard deviation
z = (5800 - 4532) / 386 ≈ 3.285
2. Use a standard normal distribution table or a statistical software to find the cumulative probability associated with the z-score. This represents the percentage of the distribution that lies below the given z-score.
3. Subtract the cumulative probability from 1 to get the percentage of the distribution that lies above the z-score.
Based on the z-score, you can look up the cumulative probability in the standard normal distribution table or use a calculator or software to find it. Let's use the second option for convenience.
Using statistical software or calculators that provide cumulative probability functions, you can find the value of P(Z < 3.285) to be approximately 0.99949.
Now, subtracting this probability from 1 gives us the percentage of months where the average monthly sales amount exceeds $5,800:
P(X > 5800) = 1 - P(Z < 3.285) ≈ 1 - 0.99949 ≈ 0.00051
So, the percentage of months that the average monthly sales amount exceeds $5,800 is approximately 0.00051 or 0.051%.