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:

Question

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.

economyst · Answer

.45 is .05 away from the mean or .05/.023 = 2.17 standard deviations away from the mean. Your stats book should have a cumulative normal distribution table. Look up 2.17. I get .9850, meaning that the probability of observing a sample where more than 45% is 1-.985 = .015=1.5%

.35 is also 2.17 standard deviations from the mean. Take it from here.

jaz · Answer

so for c. do i subtract the amounts of the two