Convert 95 pints to gallons. Round to one decimal place.

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

3 years ago

A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm,

solong [7]

They are each multiplied by a factor of 3.5
You can calculate this by taking the length of the similar prism and divide it with the first prism 14.7/4.2 = 3.5
Do this with the width and height to be sure
20.3/5.8 = 3.5
33.6/9.6 = 3.5

5 0

3 years ago

Read 2 more answers

3 over the power of 2 multiply by 3 over the power of 5

Nostrana [21]

Answer:

$3^2 \times 3^5 = 3^7$

3^2 * 3^5 = 3^7

Step-by-step explanation:

I assume you mean this:

$3^2 \times 3^5$

If so, then the rule is that when you multiply two numbers with the same base, you give the same base and add the exponents.

$3^2 \times 3^5 = 3^{2 + 5} = 3^7$

7 0

3 years ago

Can anyone help me, i will give brainiest.

laila [671]

Answer: ∠DOB: 48°

Step-by-step explanation:

1. we need an equation first. the sum of all angles (108°, n°, 2n°) is equal to 180°. we can depict this with the equation: 108°+2n°+n°=180°

2. now we can solve for the missing variable, n.

108°+3n°=180° → subtract both sides by → 3n°=72° → divide both sides by 3 → n=24°

3. now that we know that n=24°, we can solve the value of ∠DOB. we can see that ∠DOB is 2n° which we just plug the number we got for n into the equation. 2*24=48° meaning ∠DOB is 48°

hope this heped! ♡

7 0

2 years ago

Read 2 more answers

In a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?

Leokris [45]

Answer:

30

Step-by-step explanation:

94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers

7 0

3 years ago