Jen asked in Science & MathematicsMathematics · 7 years ago

# 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?

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~

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• Guy
Lv 7
7 years ago

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.