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uranmaximum [27]
2 years ago
9

How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confide

nce that the sample mean is within $2 of the population mean, and the population standard deviation is known to be $60.
Mathematics
1 answer:
kari74 [83]2 years ago
8 0

Answer:

The sample of students required to estimate the mean weekly earnings of students at one college is of size, 3458.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean (<em>μ</em>) is:

CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}

The margin of error of a (1 - <em>α</em>)% confidence interval for population mean (<em>μ</em>) is:

MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}

The information provided is:

<em>σ</em> = $60

<em>MOE</em> = $2

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

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

Compute the sample size as follows:

MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}

       n=[\frac{z_{\alpha/2}\times \sigma }{MOE}]^{2}

          =[\frac{1.96\times 60}{2}]^{2}

          =3457.44\\\approx 3458

Thus, the sample of students required to estimate the mean weekly earnings of students at one college is of size, 3458.

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Two hiking groups made the purchases shown below. What is the cost of each item. GROUP 1: 6 muffins, 12 granola bars, Total=$26.
stepladder [879]

Answer:

Price of each muffin = $1.25

Price of each granola bar = $1.6

Step-by-step explanation:

Group 1:

6 muffins, 12 granola bars

Total money paid = $26.70

Group 2:

8 muffins, 15 granola bars,

Total money paid = $34.00

To find:

Price of each item?

Solution:

Let the price of one muffin = $x

Let the price of one granola bar = $y

As per group 1, the equation can be written as:

6x+12y=26.70\\\Rightarrow x+2y=4.45 .... (1)

As per group 2, the equation can be written as:

8x+15y = 34 .... (2)

Let us use elimination method to solve for x and y.

Multiplying equation (1) with 8 and subtracting (2) from it:

16y-15y = 35.6 - 34\\\Rightarrow y = 1.6

Using equation (1):

x+3.2=4.45\\\Rightarrow x = 1.25

Therefore, the answer is:

Price of each muffin = $1.6

Price of each granola bar = $1.25

7 0
3 years ago
50 POINTS - A Builder intends placing 7 equally spaced homes on a semicircular plot. If the circle has a diameter of 400 feet, w
Ray Of Light [21]

Answer:  89.7 ft

<u>Step-by-step explanation:</u>

Find the arc length (s) of the semi-circle.  Then divide that length by 7.

s = r · θ      where r is the radius and θ is the angle in radians

s = (400 ÷ 2) · π        <em>(radius is diameter divided by 2)</em>

  = 200π

  = 628.3

The length of the arc is 628.3 ft.  Divide that by 7 to find the distance between each home.

628.3 ÷ 7 = 89.7

3 0
3 years ago
A grocery store is offering a sale on bread and soup. Khalil buys four cans of soup and
Flura [38]

Answer:

a) cblo

2)$3.44

Step-by-step explanation:

4 cans and 3 loaves=11.67

8 cans and 1 loaf= 12.89.

Set up equation:

x=cans

y=loaves

4x+3y=11.67\\8x+y=12.89 This is the answer for question A.

Multiply eq1 by 2:

8x+6y=23.34

Subtract eq3 by eq2:

5y=10.45\\y=2.09

Substitute:

8x+2.09=12.89\\8x=10.8\\x=1.35

One can of soup and one loaf of bread=

1.35+2.09 or 3.44

So:

$3.44

Hope this helps :D Please hit the crown if u can !!

6 0
3 years ago
how do I solve subtract 19 from My number and mulitply the difference by -4 , the result is -44 What is Sara number​
Lera25 [3.4K]
Saras number is 396 - 997 - 239 oop
5 0
3 years ago
Write the improper fraction as a mixed number in simplest form. 11/2
pantera1 [17]

Answer:

5 and 1/2

Step-by-step explanation: 2 goes into 11 5 times without passing it. That one that is left over would be the numerator and 2 as the demonator.

5 0
2 years ago
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