Jennifer buys four tubs of coleslaw. She serves two-fifths of each tub onto one plate.

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

I am Lyosha [343]

Answer:

(a) The proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b) The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

Step-by-step explanation:

Let <em>X</em> = number of students who read above the eighth grade level.

(a)

A sample of <em>n</em> = 269 students are selected. Of these 269 students, <em>X</em> = 224 students who can read above the eighth grade level.

Compute the proportion of students who can read above the eighth grade level as follows:

$\hat p=\frac{X}{n}=\frac{224}{269}=0.8327$

The proportion of students who can read above the eighth grade level is 0.8327.

Compute the proportion of tenth graders reading at or below the eighth grade level as follows:

$1-\hat p=1-0.8327$

$=0.1673$

Thus, the proportion of tenth graders reading at or below the eighth grade level is 0.1673.

(b)

the information provided is:

<em>n</em> = 709

<em>X</em> = 546

Compute the sample proportion of tenth graders reading at or below the eighth grade level as follows:

$\hat q=1-\hat p$

$=1-\frac{X}{n}$

$=1-\frac{546}{709}$

$=0.2299\\\approx 0.229$

The critical value of <em>z</em> for 95% confidence interval is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for the population proportion as follows:

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.229\pm 1.96\times \sqrt{\frac{0.229(1-0.229)}{709}}\\=0.229\pm 0.03136\\=(0.19764, 0.26036)\\\approx (0.198, 0.260)$

Thus, the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.198, 0.260).

5 0

3 years ago

On a particular Saturday, 60% of the visitors to an art museum were students. If 144 visited the museum, how many total visitors

Bad White [126]

Answer:

240 visitors

Step-by-step explanation:

We are given the following in the question:

Percentage of visitors that are student to art museum = 60%

Total number of students to museum = 144

We have to find the total number of visitors to the museum.

Let x be the total number of visitors to the museum.

Thus, we can write the equation:

$60\%\times x = 144\\\\\dfrac{60}{100}\times x = 144\\\\\Rightarrow x = 144\times \dfrac{100}{60}\\\\\Rightarrow x = 240$

Thus, there were 240 visitors to the art museum on that day.

6 0

3 years ago

48=3 times 2 to the power of a 56=7 times 2 to the power of bWhat are the values of a and b?a= b=

Digiron [165]

9514 1404 393

Answer:

a = 4
b = 3

Step-by-step explanation:

From your knowledge of multiplication tables, you know ...

48 = 6·8 = 3·2·2·2·2 = 3·2^4 . . . . a = 4

56 = 7·8 = 7·2·2·2 = 7·2^3 . . . . . . b = 3

8 0

3 years ago

Emily and Molly are selling pies for a school fundraiser. Customers can buy cherry pies and lemon pies. Emily sold 4 cherry pies

Natalka [10]

Answer:

<h2>cherry pie = 5</h2><h2>lemon pie =10</h2>

Step-by-step explanation:

Step one:

let cherry be x

and lemon be y

the systems of the equation for the solution is given as

4x+y=30-----------1

8x+6y=100------2

Step two:

solve the equation simultaneously by substitution we have

4x+y=30

y=30-4x

put y=30-4x in equation 2

8x+6(30-4x)=100

8x+180-24x=100

8x-24x=100-180

-16x=-80

x=80/16

x=5

put x=4 in y=30-4x

y=30-4(5).

y=30-20

y=10

5 0

3 years ago

Select the property that allows the left member of the equation to be changed to the right member. 8 + 0 = 8

lesya692 [45]

<span>identity property of addition</span>

7 0

3 years ago