Answer :
The probability that a randomly selected value is greater than 70.7 is approximately 1 - 0.6179 = 0.3821, or 38.21%.
To find the probability that a randomly selected value is greater than 70.7 in a normal distribution with a mean of 59.1 and a standard deviation of 38.7, we can use the Z-score formula.
The Z-score measures the number of standard deviations an individual value is from the mean. The formula for calculating the Z-score is:
Z = (X - μ) / σ
where Z is the Z-score, X is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a randomly selected value is greater than 70.7, so X = 70.7.
Plugging in the values into the Z-score formula, we get:
Z = (70.7 - 59.1) / 38.7
Simplifying, we get:
Z = 11.6 / 38.7
Z ≈ 0.299
Now, we need to find the probability associated with this Z-score using a standard normal distribution table or a calculator. The probability of a Z-score greater than 0.299 can be found by subtracting the probability associated with a Z-score of 0.299 from 1.
Using a standard normal distribution table or calculator, we find that the probability associated with a Z-score of 0.299 is approximately 0.6179.
Therefore, the probability that a randomly selected value is greater than 70.7 is approximately 1 - 0.6179 = 0.3821, or 38.21%.
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