Given similar terms, solve for the missing variables (x)

Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500

Alborosie

Answer:

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 500, \pi = \frac{421}{500} = 0.842$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874$

The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).

6 0

3 years ago

Multiply and divide in scientific notation

sashaice [31]

Answer:

To multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation.

Step-by-step explanation:

4 0

3 years ago

Tylan sent 3809 text messages in January. In February he sent 3115.

Lera25 [3.4K]

Answer:

Ummmm what’s the question?

Step-by-step explanation:

I will edit after you tell me what your question is.

Btw God bless you.have a great day!

7 0

3 years ago

Read 2 more answers

Please help me with the question please ASAP I’ll mark u as a brnlist <br> *2 questions

Kaylis [27]

Answer:

First answer is 76.50 and the second one is scale factor of 1/2

Step-by-step explanation: Mark brainlist or im deleting my answer :)

3 0

2 years ago

Read 2 more answers

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes

Sedbober [7]

Answer:

Maximum profit at (3,0) is $27.

Step-by-step explanation:

Let quantity of products A=x

Quantity of products B=y

Product A takes time on machine L=2 hours

Product A takes time on machine M=2 hours

Product B takes time on machineL= 4 hours

Product B takes time on machine M=3 hours

Machine L can used total time= 8hours

Machine M can used total time= 6hours

Profit on product A= $9

Profit on product B=$7

According to question

Objective function Z= $9x+7y$

Constraints:

$2x+3y\leq 6$

$2x+4y\leq 8$

Where $x\geq 0, y\geq 0$

I equation $2x+3y\leq 6$

I equation in inequality change into equality we get

$2x+3y=6$

Put x=0 then we get

y=2

If we put y=0 then we get

x= 3

Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I

Now put x=0 and y=0 in I equation in inequality

Then we get $0\leq 6$

Hence, this equation is true then shaded regoin is below the line .

Similarly , for II equation

First change inequality equation into equality equation

we get $2x+4y=8$

Put x= 0 then we get

y=2

Put y=0 Then we get

x=4

Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II

Point A and C are same

Put x=0 and y=0 in the in inequality equation II then we get

$0\leq 8$

Hence, this equation is true .Therefore, the shaded region is below the line.

By graph we can see both line intersect at the points A(0,2)

The feasible region is AOBA and bounded.

To find the value of objective function on points

A (0,2), O(0,0) and B(3,0)

Put A(0,2)

Z= $9\times 0+7\times 2=14$

At point O(0,0)

Z=0

At point B(3,0)

Z= $9\times3+7\times0=27$

Hence maximum value of z= 27 at point B(3,0)

Therefore, the maximum profit is $27.

6 0

3 years ago