The ages of students in a school are normally distributed with a mean of 16 years and a standard deviation of 1 year. Using the empirical rule, approximately what percent of the students are between 14 and 18 years old?

32%

68%

95%

99.7%

(i know its not B)

The percent of the students between 14 and 18 years old is 95% ⇒ answer C

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3

standard deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

- The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The ages of students in a school are normally distributed with

a mean of 16 years

∴ μ = 16

- The standard deviation is 1 year

∴ σ = 1

- One standard deviation (µ ± σ):

∵ (16 - 1) = 15

∵ (16 + 1) = 17

- Two standard deviations (µ ± 2σ):

∵ (16 - 2*1) = (16 - 2) = 14

∵ (16 + 2*1) = (16 + 2) = 18

- Three standard deviations (µ ± 3σ):

∵ (16 - 3*1) = (16 - 3) = 13

∵ (16 + 3*1) = (16 + 3) = 19

- We need to find the percent of the students between 14 and 18

years old

∴ The empirical rule shows that 95% of the distribution lies

within two standard deviation in this case, from 14 to 18

years old

* The percent of the students between 14 and 18 years old

is 95%

Answer Choice C is correct - 95%