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)
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%
<= 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:
100% - 1.5% - 1.5% = 97%