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