Question

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

Answer 1

@amistre64

Answer 2

@Michele_Laino

Answer 3

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

Answer 4

can you check a different problem?

Answer 5

ok!

Answer 6

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

Answer 7

Please wait I look at my tables...

Answer 8

okay

Answer 9

answer c. is right

Answer 10

what about a and b

Answer 11

answer b. 50-48.5= 1.5%

Answer 12

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

Answer 13

since we are very far from the mean

Answer 14

okay thank you!