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forsale [732]
3 years ago
14

10. Contacts. Assume that 30% of students at a university

Mathematics
1 answer:
jonny [76]3 years ago
5 0

Using the <em>normal distribution and the central limit theorem</em>, we have that:

a) A normal model with mean 0.3 and standard deviation of 0.0458 should be used.

b) There is a 0.2327 = 23.27% probability that more than one third of this sample wear contacts.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, for a <u>proportion p in a sample of size n</u>, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

In this problem:

  • 30% of students at a university wear contact lenses, hence p = 0.3.
  • We randomly pick 100 students, hence n = 100.

Item a:

np = 100(0.3) = 30 \geq 10

n(1 - p) = 100(0.7) = 70 \geq 10

Hence a normal model is appropriated.

The mean and the standard deviation are given as follows:

\mu = p = 0.3

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{100}} = 0.0458

Item b:

The probability is <u>1 subtracted by the p-value of Z when X = 1/3 = 0.3333</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.3333 - 0.3}{0.0458}

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

1 - 0.7673 = 0.2327.

0.2327 = 23.27% probability that more than one third of this sample wear contacts.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

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M= i + r ; solve for r
Alex777 [14]

Answer:

m - i = r

Step-by-step explanation:

In this question, you are solving for "r".

Solve:

M= i + r

We have to get "r" by itself, so subtract "i" from both sides.

m - i = r

Since we found what "r" is, we can't solve any further.

m - i = r would be your answer.

7 0
2 years ago
Help can somone help please.
disa [49]

Answer:

0.7

Step-by-step explanation:

5(9n-6)              

5×9n-5×6

45n-30

45n/45  -30/45

or 45n÷45-30÷45

n= 0.6666

0.7

hope dis helps!!!!!    

8 0
2 years ago
Woul I use open or close intervals for x - 1 &lt; 5
JulijaS [17]

Hi there!

You would use open intervals.

In the given inequality, the "<" sign is used, which means "greater than".

Open intervals would be used unless the inequality uses "≤" or "≥", which

mean "equal to or greater/less than". Closed brackets would be used in this

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4 0
3 years ago
PLEASE HELP MEEEEEEEEEEEEEEEEEE
DerKrebs [107]

Perimeter of the carpet = 21.8 m

Area of the carpet = 29.4 $ m^{2}

<u>Given</u>:

<em>Dimension of the living room:</em>

<em />l = 4.9 $ m\\w = 6 $ m

<em>A. </em><em>Perimeter </em><em>of the carpet = perimeter of a </em><em>rectangle</em>

Perimeter = 2(l + w)

Substitute

Perimeter = 2(4.9 + 6)\\= 21.8 $ m

Perimeter of the carpet = 21.8 m (The digits here are significant)

<em>B. </em><em>Area </em><em>of the carper = </em><em>area </em><em>of a </em><em>rectangle </em>

Area = l \times w

Substitute

Area = 4.9 \times 6\\= 29.4 $ m^{2}

Area of the carpet = 29.4 $ m^{2} (the digits here are significant)

Therefore, considering the rules of significant digits:

Perimeter of the carpet = 21.8 m

Area of the carpet = 29.4 $ m^{2}

Learn more here:

brainly.com/question/12932084

6 0
3 years ago
Which are the solutions of x2 = –13x – 4? 0, 13 0, –13 StartFraction 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma Sta
klasskru [66]

Solution of the given expression  x^2 = -13x-4 is x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}

Correct options are: Start Fraction negative 13 minus Start Root 153 End Root Over 2 End Fraction comma Start Fraction negative 13 + Start Root 153 End Root

Step-by-step explanation:

We need to find solutions of x^2 = -13x-4

We need to solve the quadratic equation and find values of x.

Solving:

x^2 = -13x-4

Rearranging the terms:

x^2+13x+4=0

Solving the quadratic equation using quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

where a = 1, b= 13 and c=4

putting values:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(13)\pm\sqrt{(13)^2-4(1)(4)}}{2(1)}\\x=\frac{-13\pm\sqrt{169-16}}{2}\\x=\frac{-13\pm\sqrt{153}}{2}\\x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}

So, Solution of the given expression  x^2 = -13x-4 is x=\frac{-13+\sqrt{153}}{2}\,\,and\,\,x=\frac{-13-\sqrt{153}}{2}

Correct options are: Start Fraction negative 13 minus Start Root 153 End Root Over 2 End Fraction comma Start Fraction negative 13 + Start Root 153 End Root

Keywords: Solving Quadratic Equations

Learn more about Solving Quadratic Equations at:

  • brainly.com/question/4460262
  • brainly.com/question/7361044
  • brainly.com/question/1414350

#learnwithBrainly

5 0
3 years ago
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