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 ru

Question

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)

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Josie 1 week 2021-09-14T23:52:13+00:00 2 Answers 0

Answers ( )

    0
    2021-09-14T23:53:44+00:00

    Answer:

    Answer Choice C is correct- 95%

    0
    2021-09-14T23:53:47+00:00

    Answer:

    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%

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