with a mean of 62 and standard deviation of 12, how would you find a proportion greater than 80 and draw it on a curve?
To find the proportion greater than 80 in a given dataset with a mean of 62 and a standard deviation of 12, you can use the concept of Z-scores and the standard normal distribution.
Step 1: Calculate the Z-score
Z-score is a measure of how many standard deviations an individual data point is away from the mean. To find the Z-score corresponding to a value of 80 in this case, you can use the formula:
Z = (X - μ) / σ
where X is the given value, μ is the mean, and σ is the standard deviation.
In this case, X = 80, μ = 62, and σ = 12. Plugging these values into the formula:
Z = (80 - 62) / 12
Z = 1.5
So, the Z-score corresponding to a value of 80 is 1.5.
Step 2: Find the proportion using a Z-table or calculator
With the calculated Z-score, you can now find the proportion using a Z-table (also called a standard normal distribution table) or a Z-score calculator. This table or calculator provides the area under the standard normal distribution curve corresponding to the given Z-score.
Since we are interested in finding the proportion greater than 80, we need to find the area to the right of the Z-score of 1.5. This represents the probability of randomly selecting a value greater than 80 from the distribution.
Step 3: Drawing the curve
To visualize the proportion greater than 80 on a curve, you can draw a standard normal distribution curve (also known as a bell curve) with the mean and standard deviation provided.
Typically, the area under the curve is shaded to represent the proportion or probability. In this case, you would shade the portion to the right of the Z-score of 1.5, indicating the proportion greater than 80.
Note: The actual curve shape and shading can be done using software like Excel, statistical calculators, or online graphing tools.