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
cricket20 [7]
2 years ago
11

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

mine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage? ​b) Assume that a recent survey suggests that about 87​% of adults have heard of the brand.
Mathematics
1 answer:
VMariaS [17]2 years ago
6 0

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that \pi = 0.87

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}

0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}

\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}

(\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2

n = 122.4

Rounding up:

He must survey 123 adults.

You might be interested in
How do I solve for FOIL
Elanso [62]

Answer:

Do the parentheses first. then the operations. Then solve

Step-by-step explanation:

4 0
2 years ago
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros for
timama [110]
The general form of a polynomial is: x² + bx + c = 0. Substituting the roots,

3² + b(3) + c = 0
3b + c = -9 --> eqn 1

(5 + √5)² + (5 +√5)(b) + c = 0
(5+√5)b + c = -30-10√5 --> eqn 2

Solving both equations simultaneously by subtracting eqn 2 from eqn 1,
(-2 - √5)b = 21 + 10√5
b = -8 - √5

Using eqn 1,
3(-8 - √5) + c = -9
-24 - 3√5 + c = -9
c = -9 + 24 + 3√5
c = 15 + 3√5

Hence, the polynomial is: <em>f(x) = x² + (-8 - √5)x + (15 + 3√5)</em>.
7 0
3 years ago
Will mark Brainliest
Ivahew [28]

Answer:

57.39

[tex]440 \: ( 1 + \frac{5t}{46 + \: {t}^{2} } ) \\ 440 \: ( \frac{6t}{46 {t}^{2} } ) \: ( \: multiply \: 440 \times 6t) \\ \frac{2640}{46} \\ = 57.39 or 57.30

8 0
2 years ago
Go math book 5th grade lesson 10.6
xxMikexx [17]

Answer:lol

Step-by-step explanation:

8 0
2 years ago
THE FIRST AND BEST ANSWER GETS BRAINLIEST
wolverine [178]
If it’s 5 points no one is gonna answer
4 0
2 years ago
Other questions:
  • PLZ HELP ASAP! Tysm!
    13·1 answer
  • Find value of x in circle O
    10·1 answer
  • After a weekend at the beach, Lisa has $274 less than she had when she left. The equation that represents this situation is e=s−
    13·1 answer
  • Look at the pic pls no silly answers
    15·2 answers
  • I need help ASAP PLEASEEE
    15·1 answer
  • 2x - 2y + 5 = 0<br> Written in slope-intercept form
    9·2 answers
  • Use the work shown below to solve.
    10·2 answers
  • 30.16 = 17.56 + 5x what is x
    9·2 answers
  • 25 points!!! I would really appreciate the help, please!!! I'll give Brainliest if you show your work, including the points that
    8·1 answer
  • What is a 120% increase?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!