Question
Find the probability using the normal distribution:
places.
places.
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability
Solution
We are asked to find
using the standard normal distribution. The probability can be expressed as
where
Using the symmetry of the normal distribution, we have
Thus,
Now, using typical values from the standard normal table:
Substitute these values into the equation:
Thus, the probability is
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Simplify this solution Mind Expander
To find the probability
First, calculate
Now, subtract these two probabilities:
So,
For a fun twist, did you know that the normal distribution is often referred to as the “bell curve” due to its shape? This distribution is pivotal in statistics because it describes how traits are distributed in a population, from height to SAT scores, making it a foundational concept in fields like psychology, biology, and economics!
If you’re diving into this topic, it’s worthwhile to check out how the normal distribution relates to the Central Limit Theorem. It states that the sum of a large number of random variables will tend to follow a normal distribution, regardless of the shape of the original distribution. This concept is vital in statistics, enabling researchers to make inferences about population parameters!
