A rectangular porch is 4 feet wide it is 3 times as long as it is wide what is the area of the porch

Schadek Silkscreen Printing Inc. purchases plastic cups and imprints them with logos for sporting events, proms, birthdays, and

Ivahew [28]

Answer:

(a) The estimated proportion of defective in the population is 0.05.

(b) The 95% confidence interval for the proportion defective cups is (2.5%, 7.5%).

(c) Zack does not needs to return the lots.

Step-by-step explanation:

Let X = number of defective cups.

The random sample of cups selected is of size, n = 300.

The number of defective cps in the sample is, X = 15.

(a)

The proportion of the defective cups in the population can be estimated by the sample proportion because the sample selected is quite large.

The sample proportion of defective cups is:

$\hat p=\frac{X}{n}=\frac{15}{300}=0.05$

Thus, the estimated proportion of defective in the population is 0.05.

(b)

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p \pm z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Compute the critical value of z for 95% confidence level as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for p as follows:

$CI=\hat p \pm z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.05 \pm 1.96\times\sqrt{\frac{0.05(1-0.05)}{300}}$

$=0.05\pm 0.025\\=(0.025, 0.075)\\$

Thus, the 95% confidence interval for the proportion defective cups is (2.5%, 7.5%).

(c)

It is provided that Zack has an agreement with his supplier that he is to return lots that are 10% or more defective.

The 95% confidence interval for the proportion defective is (2.5%, 7.5%). This implies that 95% of the lots have 2.5% to 7.5% defective items.

Thus, Zack does not needs to return the lots.

5 0

2 years ago

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $4$ times as much

oksano4ka [1.4K]

Answer: 31 : 9

Step-by-step explanation:

Assume the following:

Alice's amount = P

Bob's amount = Q

Amount received = n

If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.

P + n = 4(Q - n)

P + n = 4Q - 4n

P = 4Q - 4n - n

P = 4Q - 5n - - - - (1)

If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob

P - n = 3(Q + n)

P - n = 3Q + 3n

P = 3Q + 3n + n

P = 3Q + 4n - - - - - - (2)

Equating both equations - (1) and (2)

4Q - 5n = 3Q + 4n

4Q - 3Q = 4n + 5n

Q = 9n

Express P in terms of n, use either equation (1) or (2)

From equation 2:

P = 3Q + 4n

Substituting Q = 9n

P = 3(9n) + 4n

P = 27n + 4n

P = 31n

Alice's amount = P, Bob's = Q

Ratio = P:Q

31 : 9

5 0

2 years ago

stilt scored 5 points less than twice the number scored by dunk. together they scored 43 points. how many points were scored by

gizmo_the_mogwai [7]

Set up a system of equations:

s = 2d - 5
s + d = 43

Where 's' represents the number of points Stilt scored and 'd' represents the number of points Dunk scored.

Plug in 2d - 5 for 's' in the 2nd equation:

s + d = 43

2d - 5 + d = 43

Combine like terms:

3d - 5 = 43

Add 5 to both sides:

3d = 48

Divide 3 to both sides:

d = 16

Plug this back into any of the two equations to find 's':

s + d = 43

s + 16 = 43

Subtract 16 to both sides:

s = 27

So Dunk scored 16 points and Stilt scored 27 points.

4 0

2 years ago

Cassie has 20 bracelets. How many can she give to her sister if she wants to keep 11 or more bracelets? What repeats in the poss

Mademuasel [1]

If Cassie has 20 and wants to keep 11 then we would subtract 11 from 20.

So 20 - 11 is 9.

Her sister will get 9 bracelets.

Hope this helps!

3 0

2 years ago

bob is having a party and want to order some cake. there will be 57 guest and he wants to make sure that everyone gets a slice o

Leviafan [203]

Bob should by the 25cm cake for 18.75 each. He will need to buy 3 of these cakes in order to feed 57 guests. The total cost would be 56.25. If he were to buy the 20cm cake, he would need to purchase 5 cakes for a total of 67.50.

4 0

2 years ago