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3 July, 20:26

A sample of fifth-grade classes was studied in an article. One of the variables collected was the class size in terms of student-to-faculty ratio. The student-to-faculty ratios of the 70 fifth-grade classes sampled have a mean of 17.33 and a standard deviation of 2.36.

Complete parts (a) through (c) below.

a. x-3s

x+s

x-2s

x+2s

x+3s

Type integers or decimals. Do not round.

b. Apply Property 1 of the empirical rule to make pertinent statements about the observations in the sample At least 8 out of 70 fifth-grade classes sampled have student-to-faculty ratios between 15.36 and 17.86 Type integers or decimals. Do not round.

c. Apply Property 2 of the empirical rule to make pertinent statements about the observations in the sample. At least out of 70 fifth-grade classes sampled have student-to-faculty ratios between and Type integers or decimals. Do not round

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Answers (1)
  1. 3 July, 23:25
    0
    a)

    10.25

    19.69

    12.61

    22.05

    24.41

    b)

    P (14.97 < x < 19.69) = 0.68

    c)

    P (12.61 < x < 22.05) = 0.95

    Step-by-step explanation:

    Given:

    - Sample mean x_bar = 17.33

    - Sample mean s. d = 2.36

    Find:

    x_bar - 3s

    x_bar + s

    x_bar - 2s

    x_bar + 2s

    x_bar + 3s

    Apply Property 1 of the empirical rule to make pertinent statements about the observations in the sample At least 8 out of 70 fifth-grade classes sampled have student-to-faculty ratios between 15.36 and 17.86

    Apply Property 2 of the empirical rule to make pertinent statements about the observations in the sample. At least out of 70 fifth-grade classes sampled have student-to-faculty ratios between and Type integers or decimals.

    Solution:

    part a)

    x_bar - 3s = 17.33 - 3*2.36 = 10.25

    x_bar - 2s = 17.33 - 2*2.36 = 12.61

    x_bar - s = 17.33 - 2.36 = 14.97

    x_bar + 3s = 17.33 + 3*2.36 = 24.41

    x_bar + 2s = 17.33 + 2*2.36 = 22.05

    x_bar + s = 17.33 + 2.36 = 19.69

    part b)

    - The first property of empirical rule states that the probability of score between 1 standard deviation from the mean is 68 %. Hence,

    P (x_bar - s. d < x < x_bar + s. d) = 0.68

    P (14.97 < x < 19.69) = 0.68

    part c)

    - The first property of empirical rule states that the probability of score between 2 standard deviation from the mean is 95 %. Hence,

    P (x_bar - 2*s. d < x < x_bar + 2*s. d) = 0.95

    P (12.61 < x < 22.05) = 0.95
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