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IgorLugansk [536]

2 years ago

10

As of 2016, New York City has a population of 8.55 million and a land area of 300 square miles. Manhattan is a section of New Yo

ur City that has a land area of 23 square miles and a population of 1.64 million. How much greater is the population density of Manhattan than that of New York City?

1 answer:

sineoko [7]2 years ago

3 0

Answer: 42804 people per square mile

Step-by-step explanation:

As we know Population density = $\dfrac{Number\ of\ people}{Area}$

Given, population of New York City = 8.55 million

Area of New York City = 300 square miles

Then, population density of New York City = $\dfrac{8.55\text{ million}}{300\text{ square miles}}$

$=\dfrac{8550000}{300\text{ square miles}}=28500\text{ people per square mile}$ [1 million = 1,000,000]

Population of Manhattan = 1.64 million = 1640000

Area of Manhattan = 23 square miles

population density of Manhattan = $\dfrac{1640000}{23}\approx71304\text{ people per square mile}$

Difference = 71304 - 28500 =42804

Hence, population density of Manhattan is 42804 people per square mile greater than that of New York City.

You might be interested in

The process standard deviation is 0.27, and the process control is set at plus or minus one standard deviation. Units with weigh

mr_godi [17]

Answer:

a) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

b) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

c) For this case the advantage is that we have less items that will be classified as defective

Step-by-step explanation:

Assuming this complete question: "Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situation.

Part a

The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects."

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,0.15)$

Where $\mu=10$ and $\sigma=0.15$

We can calculate the probability of being defective like this:

$P(X$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And if we replace we got:

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

Part b

Through process design improvements, the process standard deviation can be reduced to .05. Assume the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects.

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

Part c What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

For this case the advantage is that we have less items that will be classified as defective

5 0

2 years ago

A company that packages salted and unsalted mixed nuts received a complaint that claimed that the company’s salted packages cont

Eduardwww [97]

Answer:

$H_0 : \mu_1 - \mu_2 = 0$

$H_a : \mu_1 - \mu_2 \ne 0$

Step-by-step explanation:

Let the salted package be represented with 1 and the unsalted, 2.

So:

$\mu_1:$ Mean of salted package

$\mu_2:$ Mean of unsalted package

Considering the given options, the null hypothesis is that which contains =.

So, the null hypothesis is:

$H_0 : \mu_1 - \mu_2 = 0$

The opposite of = is $\ne$ . So, the alternate hypothesis, is that which contains $\ne$

So, the alternate hypothesis is:

$H_a : \mu_1 - \mu_2 \ne 0$

4 0

2 years ago

A + b = dr, solve for a

AURORKA [14]

Hey there!

Since we don't have values for b, d, and r, we can't get a specific number for the value of a, if that makes sense. It'll be represented by these variables.

To solve, we need to make sure the equation looks like a = ? .

Subtract b from each side of the equation.

<u>a = dr - b </u>

Now we have solved for a.

Hope this helps!

6 0

2 years ago

Solve the following systems of equations.<br> 2= 2y + 5<br> | 3y - 3x = -12

ivanzaharov [21]

Answer:

x=5/2, y=-3/2. (5/2, -3/2).

Step-by-step explanation:

2=2y+5

3y-3x=-12

--------------

2-5=2y

2y=-3

y=-3/2

3(-3/2)-3x=-12

-9/2-3x=-12

3x=-9/2-(-12)

3x=-9/2+12

3x=-9/2+24/2

3x=15/2

x=(15/2)/3

x=(15/2)(1/3)

x=15/6=5/2

7 0

3 years ago

[-1/4/5] × [-7/10+0.95] - [-2/1/4]

const2013 [10]

Answer:

-2.5625

Step-by-step explanation:

<u>1)[-1/4/5] × [-7/10+0.95] - [-2/1/4] turn that into improper fractions</u>

2 1/4=9/4

which is 1 4/5(-7/10+0.95)9/4

<u>2) 1 4/5(-7/10+0.95)= 0.3125</u>

which is 0.3125-9/4

<u>3)Make into decimal form</u>

9/4 equals 2.25

which is 0.3125-2.25

which all equals -2.5625

5 0

2 years ago