IQ scores for adults aged 20 to 34 years are normally distributed according to N (110,25).Use the empirical rule to answer the following: Approximately what percent of people in this group have scores below 110?

Question

kirbykirby · Answer

So if $X$ is the scores of the people, then you are asked to find $P(X<110)$. By standardizing:
$$ P(X<110)=P\left( \frac{X-110}{5}<\frac{110-110}{5}\right)=P(Z<0)$$. Since 0 is the middle of the standard normal distribution, can you figure out how many lie below 0?

anonymous · Answer

I dont understand how this relates?

kirbykirby · Answer

Whenever you have a normal distribution, you standardize it so it has mean 0 and standard deviation 1. This way you can use a normal table to find the probabilities using the critical z-values, or if you get "nice" z-values (like 1 or 2) that correspond to the values described in the empirical rule..

But even without standardizing, you can realize that they ask for the percentage of people below 110, but 110 is the mean of your distribution. Since the normal distribution is symmetrical about the mean, 50% of the values will lie below and above the mean:

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