QuestionFind the percentage of values below in a normal distribution with mean and standard deviation .
Studdy Solution
STEP 1
Assumptions1. The distribution is approximately normal. The mean of the distribution is1593. The standard deviation of the distribution is174. We need to find the percentage of values below125
STEP 2
In a normal distribution, the percentage of values below a given value is found by calculating the Z-score of the value and then finding the area to the left of that Z-score in the standard normal distribution.
The Z-score is calculated as followswhere- X is the value we are interested in- μ is the mean of the distribution- σ is the standard deviation of the distribution
STEP 3
Plug in the values for X, μ, and σ to calculate the Z-score.
STEP 4
Calculate the Z-score.
STEP 5
Now that we have the Z-score, we can find the percentage of values below125 by looking up the Z-score in a standard normal distribution table or using a calculator with a normal distribution function.
The standard normal distribution table tells us the area to the left of a given Z-score. This area represents the percentage of values below the given value.
For a Z-score of -2, the area to the left is approximately0.0228 or2.28%.
So, approximately2.28% of values are below125.
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