Snrpatel10

Recall that in a sample of 60 Wal-Mart stores, 52 violated the NIST scanner accuracy standard. Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within .05 with 90% confidence using the large-sample method.

I really have no idea how to start, let alone do a problem like this. Thank you in advance for any and all help!

1) Suppose I flip a coin 4 times, and regard the outcome of an exp. as the sequence of heads and tails that are observed. How many sample points are there?

My answer: 16

2) Suppose that the coin is fair. For each of the sample points listed in question 1, write the down the probability that the experiment will result in that outcome.

My answer:

Pr(0 Heads, 4 Tails) = 1/16

Pr(1 Head, 3 Tails) = 1/4

Pr(2 Heads, 2 Tails) = 3/8

Pr(3 Heads, 1 Tail) = 1/4

Pr(4 Heads, 0 Tails) = 1/16

3) Flip four coins, one hundred times. Record the outcomes, and calculate sample frequencies for each of the sample points listed in question 1.

I did this and here's what I ended up getting:

(0 Heads, 4 Tails) = Occurred 7 Times out of 100 attempts

(1 Heads, 3 Tails) = Occurred 18 Times out of 100 attempts

(2 Heads, 2 Tails) = Occurred 41 Times out of 100 attempts

(3 Heads, 1 Tails) = Occurred 27 Times out of 100 attempts

(4 Heads, 4 Tails) = Occurred 7 Times out of 100 attempts

4) What is the range of the possible number of heads that can be obtained? For each possibility, determine a compound event from the sample points in question 1, and calculate a probability from your answer in question 2, and a sample frequency from you answer in question 3.

Question 4 in the one I need help with. I'm not exactly sure what the question means by determining a compound event from q1 and then using that to calculate a probability and sample frequency from Q2 and Q3 respectively. Thank you in advance!!

I know that the least squares regression line is derived by minimizing the sum of squared errors formula, where:

S = Σ [f(x) - y]², taken from

Which can be re-written as:

S = Σ [ax + b - y]²

since the least squares regression line is given by the formula: f(x) = ax + b

Minimizing the Sum of the Squared Errors formula for 'a' and 'b' respectively:

Taking the partial w/respect to a:

(∂S / ∂s) = ∑ [ 2x(ax + b - y) ]

(∂S / ∂a) = 2a∑x² + 2b∑x - 2∑xy

Taking the partial w/respect to b:

(∂S / ∂b) = ∑ 2(ax + b - y)

(∂S / ∂b) = 2a∑x + 2nb - 2∑y

Setting the two partials equal to 0 and solving for 'a' and 'b':

2a∑x² + 2b∑x - 2∑xy = 0

2a∑x + 2nb - 2∑y = 0

2a∑x² + 2b∑x = 2∑xy

2a∑x + 2nb = 2∑y

From here, I'm not exactly sure how to go about solving for a and b mainly because the ∑ is throwing me off a bit. I first tried to solve for 'b' by multiplying the second equation by a '-x' term. By doing that, I ended up with: bx - bxn = 0. As a result, the 'b' term cancels out which obviously isn't suppose to happen.

In the end, 'a' and 'b' should equal:

a = [ n∑xy - ∑x∑y ] / [ n∑x² - (∑x)² ]

b = (1/n) * [ ∑y - a∑x ]

Any and all help is always appreciated. Thanks in advance!

"The imbalance between the vast devastation nuclear weapons can inflict and any reasonable political goals has made leaders of states understandably loath to employ them."

The pair I have looks similar to this:

http://www.jcrew.com/mens_category/shorts/brokenin...

Any and all help is always appreciated!!

Definite yay for me

The Problem:

(dy/dx) = (x + 3y) / (3x + y)

The problem asks us to solve the given differential equation by using an appropriate substitution.

The Substitution I used:

y = ux

dy = u(dx) + xdu

So after plugging in ux for y and udx + xdu for dy and a bit of simplifying, I eventually got to:

[ (3 - u) / (1 - u²) ] du = [x / x²] dx

Taking the integral of both sides left me with (let "{" be the absolute value sign):

ln{1 + u} - 2ln{1 - u} = ln{x} + C

Simplifying this up a bit, I got:

ln{ (1 + u) / (1 - u)² } = ln{Cx}

After taking the exponential of both sides, I got:

(1 + u) / (1 - u)² = Cx

Plugging in y/x for u gave me:

(x + y) / x = Cx((x - y) / x)²

Multiplying both sides by x:

x + y = Cx²[(x - y)² / x²]

x²'s cancel out, leaving me with:

x + y = C(x - y)²

Now for whatever reason, that solution just doesn't seem correct to me. So if anyone could tell me where I went wrong or could just verify that the solution is indeed correct, that would be awesome. Any and all help is always appreciated.

The Problem:

(dy/dx) = (x + 3y) / (3x + y)

The problem asks us to solve the given differential equation by using an appropriate substitution.

The Substitution I used:

y = ux

dy = u(dx) + xdu

So after plugging in ux for y and udx + xdu for dy and a bit of simplifying, I eventually got to:

[ (3 - u) / (1 - u²) ] du = [x / x²] dx

Taking the integral of both sides left me with (let "{" be the absolute value sign):

ln{1 + u} - 2ln{1 - u} = ln{x} + C

Simplifying this up a bit, I got:

ln{ (1 + u) / (1 - u)² } = ln{Cx}

After taking the exponential of both sides, I got:

(1 + u) / (1 - u)² = Cx

Plugging in y/x for u gave me:

(x + y) / x = Cx((x - y) / x)²

Multiplying both sides by x:

x + y = Cx²[(x - y)² / x²]

x²'s cancel out, leaving me with:

x + y = C(x - y)²

Now for whatever reason, that solution just doesn't seem correct to me. So if anyone could tell me where I went wrong or could just verify that the solution is indeed correct, that would be awesome. Any and all help is always appreciated.

I feel like its a massive world-wide inside joke I'm left out of.

Now that the non-waiver trade deadline has past, who do y'all think came out on top/bottom?