What is the unit price for a pound of chicken if 1.5 pounds cost $3.75? Label your answer is dollars per pound.

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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

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

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

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 $ME =\pm 0.06$ 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:

$n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968$

And rounded up we have that n=170

6 0

3 years ago

A plane at an altitude of 7000 ft is flying in the direction of an island . If an angle of depression is 21 ° from the plane to

Nonamiya [84]

The horizontal distance until the plan flies over the island is 2687.05 feet approximately.

<u>Solution:</u>

Given that, A plane at an altitude of 7000 ft is flying in the direction of an island

An angle of depression is 21 degree from the plane to the island

We have to find what is the horizontal distance until the plan flies over the island

The diagram is attached below

Assume as shown in the diagram , now we can use the right angle triangle property

$\tan (21)=\frac{\text {distance between plane and point above island}}{\text {height of plane}}$

$\tan (21)=\frac{\text {distance between plane and point above island}}{7000}$

$\text { Distance between plane and point above island }=7000 \times \tan (21)$

$=7000 \times 0.38386=2687.0482$

Hence, the distance between plane and point above island is 2687.05 feet approximately.

3 0

3 years ago

a large aquarium has 6 more fish than a small aquarium. There are 19 fish in a large aquarium. How many fish are in a small aqua

Firlakuza [10]

13 fish are in the small aquarium.

5 0

3 years ago

Read 2 more answers

What is the perimeter of a lawn that is 25 feet long and 20 feet wide?

Inessa [10]

Answer:

Hey

Step-by-step explanation:

500 feet total is your answer because if you multiply the two numbers you et 500

7 0

3 years ago

Find the solutions to x2 = 20.

Gemiola [76]

Answer:

B.

Step-by-step explanation:

$x^2=20; \ => \ \left[\begin{array}{ccc}x=\sqrt{20} \\x=-\sqrt{20} \end{array} \ => \ \left[\begin{array}{ccc}x=2\sqrt{5} \\x=-2 \sqrt{5} \end{array}$

3 0

3 years ago