The distribution of cholesterol levels in teenage boys is approximately normal with u=170 and o=30. Levels above 200 warrent attention. Find the probability that boy has a cholesterol level greater than 225.
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 the Z score you calculate.
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To find the probability that a teenage boy has a cholesterol level greater than 225, we need to calculate the area under the normal curve to the right of 225.
First, we need to standardize the value of 225 using the formula:
Z = (X - u) / o
Where:
Z is the standard score (the number of standard deviations from the mean)
X is the value we want to standardize (225 in this case)
u is the mean of the distribution (170 in this case)
o is the standard deviation of the distribution (30 in this case)
Substituting the values into the formula, we get:
Z = (225 - 170) / 30
Z = 55 / 30
Z ≈ 1.8333
Next, we need to find the area under the normal curve to the right of Z = 1.8333. We can do this by looking up the Z-score in a standard normal distribution table or using statistical software.
Using a standard normal distribution table, we find that the probability of getting a Z-score greater than 1.8333 is approximately 0.0336.
Therefore, the probability that a teenage boy has a cholesterol level greater than 225 is approximately 0.0336 or 3.36%.