In a normal distribution, the mean is 20

Sydney Petitclerc

Sydney Petitclerc

Answered question

2022-04-28

In a normal distribution, the mean is 20 and the standard deviation 
was 5.  What percentage of data has a value  greater that 24?

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-05-02Added 556 answers

Let X be a random variable following a normal distribution with mean μ = 20 and standard deviation σ = 5. We want to find the percentage of data that has a value greater than 24, i.e. we need to calculate the probability P(X > 24).
We can standardize the variable X to obtain a standard normal distribution with mean 0 and standard deviation 1, by using the formula:
Z=Xμσ
Substituting the values we have:
Z=24205=0.8
We can use a standard normal distribution table or a calculator to find the probability that a standard normal variable is greater than 0.8. Using a standard normal distribution table, we find that:
P(Z>0.8)0.2119
Therefore, the percentage of data that has a value greater than 24 is:
21.19%
Note that this is an approximation since we used a table to find the probability. A more accurate result can be obtained using a calculator or statistical software.

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