Probability with the Z-score?

Suppose in a recent national election 40% of the voters were men. If a random sample of 25 voters were selected, what is the probability that more than 10 but less than 20 were women?

I think I know my z-score is 1.53, but how do I get that z-score by going through the formulas? Would I use the sample mean z-score or population?

Show me please :-)

Update:

I really, Reealllly appreciate your assistance on this question. I have all of these formulas and can't seem to figure out, when to use the darn things! The calculations as well as showing your work was magtastic!

Thanks Buddy~

1 Answer

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  • Guy
    Lv 7
    7 years ago
    Favorite Answer

    Are you supposed to use the normal approximation to the binomial?

    60% of the voters were women. The question asks for "more than 10 but less than 20", which translates to "between 11 and 19, inclusive".

    The actual probability would be (using a TI-83): binomcdf(25,.6,19) - binomcdf(25,.6,10) = .9362462771

    Now let's do the normal approximation. Remember to use the continuity correction.

    mean = .6(25) = 15

    standard deviation = sqrt(25*.6*.4) = 2.45

    P(10.5 < x < 19.5)

    = P[(10.5 - 15)/2.45 < z < (19.5 - 15)/2.45]

    = P(-1.84 < z < 1.84)

    = normalcdf(-1.84,1.84) = .9342318831

    As you can see, the normal approximation of .9342 is very close to the actual probability of .9362.

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