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Mathematics 32 Online
OpenStudy (anonymous):

can you check my work? What conditions (and theorem) must be met in order for a sampling distribution of means to be approximated by a normal distribution? answer: the central limit theorem population distribution is normal population distribution is symmetric, unimodal, without outliers, and the sample size is 15 or less population distribution is moderately skewed, unimodal, without outliers, and the sample size is between 16 and 40 sample size is greater than 40, without outliers

OpenStudy (anonymous):

@amistre64

OpenStudy (anonymous):

@Michele_Laino

OpenStudy (michele_laino):

I'm sorry I don't remember the central limit theorem

OpenStudy (anonymous):

can you check a different problem?

OpenStudy (michele_laino):

ok!

OpenStudy (anonymous):

An SRS of 400 American adults is asked, "What do you think is the most serious problem facing our schools?" Suppose that in fact 30% of all adults would answer drugs if asked this question. The proportion p-hat of the sample who answer drugs will vary in repeated sampling. In fact, we can assign probabilities to values of p-hat using the normal density curve with mean 0.3 and standard deviation 0.023. Use this density curve to find the probabilities of the following events: a) At least half of the sample believes that drugs are the schools' most serious problem. b) Less than 25% of the sample believes that drugs are the most serious problem. c) The sample proportion is between 0.25 and 0.35. a)normalcdf(0.5,1,0.3,0.023)=1.74712531^-18 P(X ≥ .5) = P((X - 0.3)/0.023 ≥ (.5 - .3)/.023) = P(Z ≥ 8.69) = P(Z ≤ - 8.69) = 0 b) normalcdf(0,.25,.3,.023)=.0148557801 P(X ≤ .25) = P((X - .3)/.023 ≤ (.25 - .3)/.023) = P(Z ≤ - 2.17) = .015003 c) P(.25 ≤ X ≤ .35) = P((.25 - .3)/.023 ≤ (X - .3)/.023 ≤ (.35 - .3)/.023) = P( -2.17 ≤ Z ≤ 2.17) = P(Z ≤ 2.17) - P(Z ≤ - 2.17) = .984997 - .015003 = .969994

OpenStudy (michele_laino):

Please wait I look at my tables...

OpenStudy (anonymous):

okay

OpenStudy (michele_laino):

answer c. is right

OpenStudy (anonymous):

what about a and b

OpenStudy (michele_laino):

answer b. 50-48.5= 1.5%

OpenStudy (michele_laino):

answer a. is right, namely the requested probability is zero

OpenStudy (michele_laino):

since we are very far from the mean

OpenStudy (anonymous):

okay thank you!

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