Question

Suppose that 44% of all Americans approve of the job our President is doing. The most recent Gallup poll consisted of a random sample of 1400 American adults.

a) What is the mean of the sampling distribution?
b) What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?
c) Describe the normal approximation for this sampling distribution (don't forget to justify this). You can simply write as N (mean, standard deviation).

Answer 1

d) What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%?

Answer 2

@dumbcow ?

Answer 3

I suck at stats :( sorry

Answer 4

I got this for a and b, @dumbcow . But I'm not sure if they're right. and i don't understand c and d.

Answer 5

well for a poll, you just answer yes or no.... so how to determine the mean and std dev?
im drawing a blank

Answer 6

How do I answer c?

Answer 7

what is your answer for a) and b) maybe that will jog my memory

Answer 8

i got (a) mean=n*p
=0.44*1400
=616

(b) standard deviation= sqrt(n*p*q)
= sqrt (1400*(0.44)* (1 - 0.44)
=18.57 <--

(c)

Answer 9

@dumbcow is that right

Answer 10

sorry i got distracted .... yes thats correct
so the Normal distribution is
N(616, 18.57)

Answer 11

Ok. so C is N(616, 18.57) ?

Answer 12

@dumbcow what is (d) and how did u find it?

Answer 13

@dumbcow
when you're done here, can you come back to my post? :)

Answer 14

yes

for part d) you have to use the Normal distribution to find probability that reults from poll are within 41% and 47% approval rating

translate this to a range from 574 to 658

find z-score for 658
--> (658-616)/18.57 = 2.26

find z-score for 574
--> (574-616)/18.57 = -2.26

use table to look up probabilities
P(Z < 2.26) - P(Z < -2.26)