Please help will brainliest all please

An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

monitta

Answer:

a) n =1623

b) $ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken

$\hat p=0.19$ estimated proportion of customers are not satisfied with the service provided by the local dealer

Confidence =0.96 or 96%

Me= 0.02 represent the margin of error

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 96% of confidence, our significance level would be given by $\alpha=1-0.96=0.04$ and $\alpha/2 =0.02$ . And the critical value would be given by:

$z_{\alpha/2}=-2.0538, z_{1-\alpha/2}=2.0538$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.19(1-0.19)}{(\frac{0.02}{2.0538})^2}=1622.912$

And rounded up we have that n=1623

Part b

The margin of error is given by:

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

So then if w replace the value of n obtained from part a we got:

$ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

3 0

2 years ago

Brian is selling cookies at a bake sale. He earns $2.75 for each bag of cookies he sells. Write an equation to represent this sc

sesenic [268]

Let C equal bags of cookies
Let M equal money earned

2.75c=m

Probably not enough sorry if it isn't

5 0

3 years ago

Read 2 more answers

Consider the following series. 1 9 1 18 1 27 1 36 1 45 Determine whether the series is convergent or divergent. Justify your ans

Vedmedyk [2.9K]

Answer:

Diverges; the limit of the terms, an, is not 0 as n goes to infinity

Step-by-step explanation:

Convergence of Infinite Series

The series is given as the terms

1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...

For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.

Our series has two clearly different sequences, which define it as a piecewise general term:

If n is odd, then

$a_n=1$

Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is

$a_n=9+9(n/2-1)=4.5n$

if n is even.

If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.

The limit of the function

$a_n=1$

is 1 when n goes to infinity. Since it's not 0, this piece is not convergent and the entire series isn't either.

But it goes worse because of the limit of the second piece

$a_n=4.5n$

when n goes to infinity is infinite.

The answer is

Diverges; the limit of the terms, an, is not 0 as n goes to infinity

8 0

2 years ago

A film start at 17:15 and finish at 1 hour and 45 minutes later. what time did it finish?

vova2212 [387]

It ended at 19:00 or at 7 pm

4 0

2 years ago

Y=log4x how do I work out this problem

olganol [36]

I can’t do math right now but plug it into a graphing calculator (after pressing the “Y=“ button) and then press graph and you should be good

5 0

2 years ago