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BaLLatris [955]
3 years ago
13

The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approxima

tely what percent of the students are between 14 and 18 years old?
Mathematics
2 answers:
worty [1.4K]3 years ago
8 0

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.

z=\frac{x-\mu}{\sigma}

z=\frac{14-15}{2}

z=\frac{-1}{2}

z=-0.5

Similarly, we will find the z-score corresponding to 18.

z=\frac{18-15}{2}

z=\frac{3}{2}

z=1.5

Now we will find the probability of getting a z-score between -0.5 and 1.5 that is P(-0.5.

P(-0.5

Using normal distribution table, we will get:

P(-0.5

P(-0.5

Let us convert 0.62465 into percentage.

0.62465\times 100\%=62.465\%\approx 62.5\%

Therefore, approximately 62.5\% of the students are between 14 and 18 years old.

Vanyuwa [196]3 years ago
4 0

Answer:

62.47%

Step-by-step explanation:

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