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Violence in School, I An SRS of 400 American adults is asked “What do you think is the most serious problem facing our schools?” Suppose that in fact 40% of all adults would answer “violence” if asked this question. The proportion p of the sample who answers “violence” will vary in repeated sampling. In fact, we can assign probabilities to values of p using the normal density curve with mean 0.4 and standard deviation 0.023. Use the density curve to find the probabilities of the following event:

a.At least 45% of the sample believes that violence is the school’s most serious problem.


b.Less than 35% of the sample believes that violence is the most serious problem.


c.The sample proportion is between 0.35 and 0.45.

  • ap stats -

    So, you are assuming a true population with a normal distribution of 0.4; 0.023)

    A)
    Convert 0.45 to a Z score: (0.45 - 0.40) / 0.023 = +2.17
    Look up on a z-table chart. Greater than +2.17 yields .0150 = 1.5%

    B)
    <= 0.35 has the exact opposite Z score: (0.35 - 0.40) / 0.023 = -2.17
    Less than -2.17 yields .0150 = 1.5% (same answer as A)

  • ap stats -

    Forgot C. That's probably obvious after you have A + B:

    C)
    100% - 1.5% - 1.5% = 97%

  • ap stats -

    23

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