1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Temka [501]
2 years ago
10

At a university, 60% of the 7,400 students are female. The student newspaper reports the results of a survey of a random sample

of 50 students about various topics involving alcohol abuse. They report that their sample contained 26 females. Let X be a random variable such that x = 1 denotes female and x = 0 denotes male. Consider the sampling distribution of the sample proportion of females in samples of size 50. State the mean and standard error for this sampling distribution.
Mathematics
1 answer:
omeli [17]2 years ago
4 0

Given Information:

Population mean = p  = 60% = 0.60

Population size = N = 7400

Sample size = n = 50

Required Information:

Sample mean = μ = ?

standard deviation = σ = ?

Answer:

Sample mean = μ = 0.60

standard deviation = σ = 0.069

Step-by-step explanation:

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

50*0.60 ≥ 10

30 ≥ 10 (satisfied)

n(1 - p) ≥ 10

50(1 - 0.60) ≥ 10

50(0.40) ≥ 10

20 ≥ 10  (satisfied)

The mean of the sampling distribution will be same as population mean that is

Sample mean = p = μ = 0.60

The standard deviation for this sampling distribution is given by

\sigma = \sqrt{\frac{p(1-p)}{n} }

Where p is the population mean that is proportion of female students and n is the sample size.

\sigma = \sqrt{\frac{0.60(1-0.60)}{50} }\\\\\sigma = \sqrt{\frac{0.60(0.40)}{50} }\\\\\sigma = \sqrt{\frac{0.24}{50} }\\\\\sigma = \sqrt{0.0048} }\\\\\sigma =  0.069

Therefore, the standard deviation of the sampling distribution is 0.069.

You might be interested in
Please solve! (20 points)<br><br> 3(14m + m)
IgorC [24]

Answer:

43m

Step-by-step explanation:

3(14m+m)

42m+3m

45m

7 0
3 years ago
Read 2 more answers
What is the volume of this rectangular prism?
ollegr [7]

Answer:

57,600cm {}^{2}

<em><u>Solving steps:</u></em>

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

=> 40 cm{}^{2} × 30cm{}^{2} × 48 cm{}^{2}

multiply all the numbers

=> 57,600cm{}^{2}

Hi hi hi hi

8 0
2 years ago
Read 2 more answers
Which of these is equivalent to 1 over x to the power of 5 ? 1 fifth x negative x to the power of 5 x to the power of 5 x to the
Kisachek [45]

Answer:

x^-5 = x to the power of negative 5

Step-by-step explanation:

Which of these is equivalent to 1 over x to the power of 5 ?

Mathematically this is expressed as

(1/x)⁵

We have a rule when it comes to expressing power

(1/a)^b = a^-b

Hence, applying this rule to our question

(1/x)⁵ = (1/x)^5

= x^-5

This is written in words as:

x to the power of negative 5

5 0
3 years ago
Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum. (To clarify, 1/2 is a fraction *x^
ahrayia [7]
y= -\frac{1}{2} x^{2}-1 is a quadratic function, so its graph is a parabola.

Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.

That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.

for x=0, y=-1. So the vertex is (0, -1)

The coefficient of x^{2} is negative. This means that the parabola opens downwards, so the vertex is a maximum.


Answer: (0, -1) , maximum (none of the choices)
5 0
3 years ago
X+y+z=12<br> 6x-2y+z=16<br> 3x+4y+2z=28<br> What does x, y, and z equal?
lianna [129]

Answer:

x = 20/13 , y = 16/13 , z = 120/13

Step-by-step explanation:

Solve the following system:

{x + y + z = 12 | (equation 1)

6 x - 2 y + z = 16 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Swap equation 1 with equation 2:

{6 x - 2 y + z = 16 | (equation 1)

x + y + z = 12 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Subtract 1/6 × (equation 1) from equation 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+(4 y)/3 + (5 z)/6 = 28/3 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Multiply equation 2 by 6:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

3 x + 4 y + 2 z = 28 | (equation 3)

Subtract 1/2 × (equation 1) from equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

0 x+5 y + (3 z)/2 = 20 | (equation 3)

Multiply equation 3 by 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+8 y + 5 z = 56 | (equation 2)

0 x+10 y + 3 z = 40 | (equation 3)

Swap equation 2 with equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+8 y + 5 z = 56 | (equation 3)

Subtract 4/5 × (equation 2) from equation 3:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+(13 z)/5 = 24 | (equation 3)

Multiply equation 3 by 5:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+13 z = 120 | (equation 3)

Divide equation 3 by 13:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y + 3 z = 40 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Subtract 3 × (equation 3) from equation 2:

{6 x - 2 y + z = 16 | (equation 1)

0 x+10 y+0 z = 160/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Divide equation 2 by 10:

{6 x - 2 y + z = 16 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Add 2 × (equation 2) to equation 1:

{6 x + 0 y+z = 240/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Subtract equation 3 from equation 1:

{6 x+0 y+0 z = 120/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Divide equation 1 by 6:

{x+0 y+0 z = 20/13 | (equation 1)

0 x+y+0 z = 16/13 | (equation 2)

0 x+0 y+z = 120/13 | (equation 3)

Collect results:

Answer:  {x = 20/13 , y = 16/13 , z = 120/13

8 0
3 years ago
Other questions:
  • Solve this linear equation <br> 2(x+6)&lt;3x+8
    15·1 answer
  • Find the product of 2/3 x 2/3
    15·1 answer
  • Brenda needs to bake 12 cakes for a bake sale. Each cake requires 2 3/4 cups of flour. What is a reasonable estimate of the tota
    5·1 answer
  • A shuttle service charges each customer $10.00 for a ride from the airport
    15·1 answer
  • If an object has a mass of 120 grams and a volume of 10 ml, what is its density?
    7·1 answer
  • Which rectangle is similar to a rectangle 12 inches wide and 18 inches long
    6·1 answer
  • The relation R is shown below as a list of ordered
    10·1 answer
  • Solve for the variable<br> 7x = -35
    6·2 answers
  • I’ve been stuck on this question since beginning of my freshman year! Someone please explain how to do this please??!
    9·1 answer
  • Finn and Ellie sell oranges at a produce stand. Finn earns $5 for each crate of oranges he sells. At the end of the week, Ellie
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!