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We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.
We are asked to find the percentage of students that are between 14 and 18 years old.
First of all, we will find z-score corresponding to 14 and 18 using z-score formula.
Similarly, we will find the z-score corresponding to 18.
Now we will find the probability of getting a z-score between and
that is
.
Using normal distribution table, we will get:
Let us convert into percentage.
Therefore, approximately of the students are between 14 and 18 years old.