What is z equal too ? please help me !!! thanks 10 points asap !!!

alisha [4.7K]

#21)
<span>Using Pythagorean Theorem a^2 + b^2 = c^2
so
</span>a^2 = c^2 - b^2

x^2 = 42^2 - 38^2
x^2 = 1764 - 1444
x^2 = 320
x =√320
x = √(64 * 5)
x = 8√5

8 0

3 years ago

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Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

7 0

3 years ago

WORTH 25 POINTS LAST QUESTION PLEASE ANSWER WILL MARK BRAINLIEST IF RIGHT

Gekata [30.6K]

Answer:

290

Step-by-step explanation:

Surface area=2(wl+hl+hw), 2(25+60+60), 145*2, 290

4 0

3 years ago

U

neonofarm [45]

Answer:

A, B, C

Step-by-step explanation:

x is in the intersection of sets B and C, in set B, in set C, in the union of sets B and C, in the union of sets A and C

Answer: A, B, C

3 0

4 years ago

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A random sample of 10161016 adults in a certain large country was asked "Do you pretty much think televisions are a necessity o

Korolek [52]

Answer:

0.509

Step-by-step explanation:

Given that a random sample of 1016 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?"

Of the 1016 adults surveyed, 517 indicated that televisions are a luxury they could do without.

To find out the point estimate of population proportion of adults in the country who believe that televisions are a luxury they could do without.

We find that point estimate is nothing but sample proportion

Sample proportion = favourably voters/total people surveyed

= $\frac{517}{1016} \\=0.5088\\=0.509$

6 0

3 years ago