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
DochEvi [55]
3 years ago
6

A study on students drinking habits wants to determine the true average number of alcoholic drinks all fsu undergraduate student

s who are members of a fraternity or sorority have in a one week period. We know from preliminary studies that the standard deviation is around 2.6. How many students should be sampled to be within 0.25 drinks of population mean with 95% probability?
Mathematics
1 answer:
Sedbober [7]3 years ago
4 0

Answer:

416

Step-by-step explanation:

Standard deviation is 2.6

Margin error for the problem is 0.25

Probability 95%, that means thet the siginficance level α is 1 – p

α = 1 – 0.95 = 0.05

margin of error (ME) can be defined as follows

ME = Z(α/2) * standard deviation/ √n

Where n is the sample size

Z(0.05/2) = Z(0.025)

Using a z table Z = 1.96

Now, replacing in the equation and find n

.25 = 1.96 * 2.6/ √n

0.25 = 5.096/√n

√n = 5.096 /0.25

√n = 20.38

n = 20.38^2

n = 415.5 = 416

You might be interested in
One of the relatively uncommon instances in which researchers know the population standard deviation is in the case of the Intel
Phoenix [80]

Answer:

90% confidence interval for the mean IQ score in this community is [106.58 , 109.42].

Step-by-step explanation:

We are given that in general, the average IQ score in large, diverse populations is 100 and the standard deviation is 15.

Suppose that your sample of 300 members of your community gives you a mean IQ score of 108.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

                        P.Q. = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean IQ score = 108

            \sigma = population standard deviation = 15

            n = sample of members = 300

            \mu = population mean IQ score

<em>Here for constructing 90% confidence interval we have used One-sample z test statistics because we know about population standard deviation.</em>

<em />

So, 90% confidence interval for the population mean, \mu is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                of significance are -1.645 & 1.645}  

P(-1.645 < \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } < 1.645) = 0.90

P( -1.645 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X -\mu} < 1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

P( \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

<u>90% confidence interval for</u> \mu = [ \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ]

                                      = [ 108-1.645 \times {\frac{15}{\sqrt{300} } } , 108+1.645 \times {\frac{15}{\sqrt{300} } } ]

                                      = [106.58 , 109.42]

Therefore, we can be 90% confident that the mean IQ score in this community lies between 106.58 and 109.42.

8 0
3 years ago
Identify the isosceles triangle below along with the base angles
Svetradugi [14.3K]
Part A:

From the figure shown.

The measure of line TH = 14' 72" = 14' + 72" / 12 = 14' + 6' = 20'

Given that the measure of line HI = 20'

Thus, triangle THI is an isosceles triangle with line TI as the base.



Part B:

To find the base angles we use the Pythagoras theorem.

Recall that the perpendicuar bisector of an isosceles triangle divides the triangle into two equal right triangles.

Dividing the base into two gives 22.5' / 2 = 11.25'

Thus, the perpendicular bisector divides the isosceles triangle into two equal right triangles with base of 11.25' and hypothenus of 20'.

By pythagoras theorem,

\cos\theta= \frac{11.25}{20} =0.5625 \\  \\ \theta=\cos^{-1}0.5625=\bold{55.77^o}

Therefore, the base angles is 55.77 degrees.
8 0
3 years ago
When solving equation which is the best first step to begin to simplify the equation -2(x+3)=-10
LiRa [457]

Answer:

Step-by-step explanation:

Alright, lets get started.

The given equation is :

-2(x+3)=-10

If we divide the equation with -2 in both sides

\frac{-2(x+3)}{-2}=\frac{-10}{-2}

(x+3)=5

x+3=5

Subtract 3 in both sides

x+3-3=5-3

x=2

So, the first step of simplifying equation is divide equation with -2.  :  Answer

Hope it will help :)

3 0
3 years ago
Read 2 more answers
Help Me Please!!!! I don’t get it
gtnhenbr [62]

Answer/Step-by-step explanation:

In mathematics, there's an order to follow in solving calculations like the problems given above. The acronym, PEDMAS illustrates or makes us remember which order to follow. The acronym stands for:

P - Parenthesis. Given any problem to solve, first, solve any operation within a parenthesis. That is, expressions that are grouped together.

E - Exponents. Next in line of priority order is to solve expressions involving exponents.

D - Division

M - Multiplication

A - Addition, and

S - Subtraction.

Now, solve each expression given in the correct order of operation using PEDMAS:

10 - 3³ ÷ 9

10 - 27 ÷ 9

10 - 3

= 7 (the order of operation is EDS = Exponent, Division, and lastly, Subtraction)

7² ÷ (4 + 3)

7² ÷ 7

49 ÷ 7

= 7 (order of operation = PED)

7 × 5 - 2²

7 × 5 - 4

35 - 4

= 31 (EMS)

(6 + 2²) × 10

(6 + 4) × 10

10 × 10

= 100 (PM)

3 × 6 + 8²

3 × 6 + 64

18 + 64

= 82 (EMA)

4³ - 10 ÷ 5

64 - 10 ÷ 5

64 - 2

= 32 (EDS)

3² × 2 - 9

9 × 2 - 9

18 - 9

= 9 (EMS)

9 × 3² - 8

9 × 9 - 8

81 - 8

= 73 (EMS)

6² ÷ 3 - 5

36 ÷ 3 - 5

12 - 5

= 7 (EDS)

(9 - 5)² ÷ 4

(4)² ÷ 4

16 ÷ 4

= 4 (PED)

8 0
3 years ago
The area of a circle is 16 π cm 2 . What is the circle's circumference?
Andrej [43]
A=piR^2
16pi=piR^2    So R=4cm

C=2piR
C=8pi cm

5 0
3 years ago
Other questions:
  • A pyramid-shaped vat has square cross-section and stands on its tip. The dimensions at the top are 2 m × 2 m, and the depth is 5
    10·1 answer
  • Graph the system of equations. y = -x + 3 y = -4x -6<br><br><br>NEED HELL ASAP
    5·2 answers
  • Ben's ride is 7/8 mile.Antonio's ride is 3/4 ride. Who has a longer ride?
    11·2 answers
  • The Mexican Hot Chocolate Recipe makes 2 cups of hot chocolate per batch. 1 serving is equal to 1 cup.
    15·1 answer
  • Beth is solving this equation: 1/x + 3= 3/x
    12·1 answer
  • 7. Find the length of HP.<br> 12<br> P<br> 9<br> H
    7·2 answers
  • BRAINILEST PLZZZZZzzzzz
    7·1 answer
  • Marty has read 32% of his 400-page library book. How many pages has Marty read?
    15·1 answer
  • Solve for the distance between the points (4, 4) and (1, -3).
    5·1 answer
  • Help!! pls i mark brainly answer
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!