ap stats
posted by bobby on .
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.

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 ztable 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) 
Forgot C. That's probably obvious after you have A + B:
C)
100%  1.5%  1.5% = 97% 
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