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
weeeeeb [17]
3 years ago
14

9.4 The heights of a random sample of 50 college stu- dents showed a mean of 174.5 centimeters and a stan- dard deviation of 6.9

centimeters. (a) Construct a 98% confidence interval for the mean height of all college students. (b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centime- ters?
Mathematics
1 answer:
gladu [14]3 years ago
8 0

Answer:  a) (176.76,172.24), b) 0.976.

Step-by-step explanation:

Since we have given that

Mean height  = 174.5 cm

Standard deviation = 6.9 cm

n = 50

we need to find the 98% confidence interval.

So, z = 2.326

(a) Construct a 98% confidence interval for the mean height of all college students.

x\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=(174.5\pm 2.326\times \dfrac{6.9}{\sqrt{50}})\\\\=(174.5+2.26,174.5-2.26)\\\\=(176.76,172.24)

(b) What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5 centime- ters?

Error would be

\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{6.9}{\sqrt{50}}\\\\=0.976

Hence, a) (176.76,172.24), b) 0.976.

You might be interested in
Could someone help plz
Komok [63]

Answer:

The radius of the sphere is approximately 62.71 cm

Step-by-step explanation:

The question relates to the definition of a sphere

The given parameters are;

The distance between the sharp parallel blades through which the sphere is rolled = 77 centimeters

The radii of the circular faces left by cutting the sphere with the blade = 39 cm  and 60 cm

From the triangles formed by the cross-section of the sphere, we have;

AB ║ DE Given

∠A ≅ ∠E, ∠D ≅ ∠B Alternate angles

∠C ≅ ∠C by reflective  property

∴ ΔABC ~ ΔDCE by Angle-Angle similarity theorem

CF/CG = AB/DE = 78/120 = 13/20

CF = CG × 13/20

CF + CG = 77

∴ CG × 13/20 + CG = 77

33·CG/20 = 77

∴ CG = 140/3

CF = 13/20 × CG = 13/20 × 140/3 = 91/3

CF = 91/3

The diameter of the sphere AE = AC + EC

By Pythagoras's theorem

AC = √(FA² + CF²) = √(39² + (91/3)²) = 13·√(130)/3

EC = √(CG² + GD²) = √((140/3)² + 60²) = 20·√(130)/3

∴ AE = AC + EC = 13·√(130)/3 + 20·√(130)/3 = 11·√(130)

The diameter, 'D', of the sphere, AE = 11·√(130)

The radius of the sphere = D/2 = 11·√(130)/2 ≈ 62.71 cm

7 0
2 years ago
Sally has decided to spend some time over two days soving math problems. She figures that on the first day she wil be able to so
erastova [34]

A system of equations for this would be

19x + 11y = 273

and

12x + 17y = 283.

X is the amount of minutes to solve one long division problem and y is the amount of minutes to solve a graphing problem.

How To Solve This System of Equations.

Multiply both by 17 and 11 respectively for them to have the greatest common factor for y. So now both equations are:

323x + 187y= 4641

132x + 187y= 3113.

Subtract both equations and you have left:

191x = 1528.

Divide both sides by 191 and you find x.

X = 8.

Answer

It takes Sally 8 minutes to do one Long Division Problem.


Hope this helped. ;)

6 0
3 years ago
Read 2 more answers
Let f(x) = ............
34kurt

Answer:

So first lets find g(-1)

so we plug in the answers:

-2 * -1 ^2 -4

-2*1-4 = -2-4 =

-6

Now lets solve for f(-2)

-2^2-3

4-3=1

-6+1 = 5

3*5 = 15

Im getting answer of 15 but it shows -15 or something, so I dont know if I got it wrong or if its like a dash then the answer.

3 0
3 years ago
Simplify: −3 • −26<br><br> A. −78<br> B. −68<br> C. 68<br> D. 78
hammer [34]
-3 x -26 = 78

meaning the answer is D.

The reason the answer is D, is because two negatives when multiplied or divided become positive. Only when multiplied or divided does this occur.
3 0
1 year ago
Help me pls!<br> find x and hurry im under a time limit
Licemer1 [7]

Answer:

x = 13

Step-by-step explanation:

Using the 48° angle, we find out that the angle opposite of angle y° is also 48° according to the corresponding angles theorem. Then, you would subtract 48 from 180 to get the degrees of angle y, which would be 132°. Next, you need to subtract 132 from 180 to get the angle measure of the (5x - 17)° angle. (180 - 132 = 48) Once you have done that, all you have to do now is figure out what value of x makes it equal to the degree measure you found by subtracting 132 from 180. I tried it with x = 13, which came out as a correct answer. So x must be 13.

(5x - 17)°

(5(13) - 17)°

(65 - 17)°

(48)°

48°

The angle equals 48° and x equals 13.

4 0
2 years ago
Read 2 more answers
Other questions:
  • A path is 3 feet wide and is paved Weight square brakes that are 3 inches wide. How many bricks wide is the path
    5·1 answer
  • What is the combined mass of earth and the moon
    8·2 answers
  • What is 75/54 simplified
    8·1 answer
  • Is this all correct?
    12·1 answer
  • The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 138 138. If s
    15·2 answers
  • While Mary Corens was a student at the University of Tennessee, she borrowed $14,000 in student loans at an annual interest rate
    5·1 answer
  • Ughhh can someone help its so confusing
    11·1 answer
  • 2/3w = 3/4 what’s the equation?
    13·2 answers
  • Solve the inequality and describe the solution set.<br> y–6≥12
    9·1 answer
  • A sphere has a volume of 1 cubic foot. What is the approximate diameter of the sphere?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!