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VashaNatasha [74]
2 years ago
13

. Suppose that we want to estimate the true proportion of defectives in a very large shipment of adobe bricks, and that we want

to be at least 95% confident that the error is at most 0.04. How large a sample will we need if:
Mathematics
1 answer:
wlad13 [49]2 years ago
8 0

Answer:

A sample of 601 bricks will be needed.

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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

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

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

How large a sample will we need?

A sample of n bricks will be needed.

n is found when M = 0.04.

We have no estimate for the proportion of defective bricks, so we work with the worst case scenario, which is M = 0.04

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

0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.04\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.04}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.04})^{2}

n = 600.25

Rounding up

A sample of 601 bricks will be needed.

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Volgvan

Answer:

1 out of 8

Step-by-step explanation:

If you flip a coin there are eight possible outcomes:

HHH

HHT

HTT

TTT

THH

TTH

THT

HTH

SO the probability of getting all heads is 1 over 8.

Hope this helps

5 0
3 years ago
Which of the following statements is true?
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Answer:

Step-by-step explanation:

Option C a right triangle is the correct answer

6 0
2 years ago
Julie spends 3/4 hour studying on Monday and 1/6 hour studying on Tuesday. How many hours does Julie study on the two days? (A 1
alex41 [277]
Equation: 3/4 + 1/6

3/4 = 18/24
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3 years ago
What is the diameter of the cylinder if the height is 13, and the volume is 1256? Use 3.14 for pi.
Sergio039 [100]
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1256 = (3.14) x (r)² x (13)

1256 = 40.82r²

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r² = 30.769

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8 0
3 years ago
You are given a 16-bit binary integer X= (1110 0100 0111 1010)2 . Convert X to decimal if:
podryga [215]

Step-by-step explanation:

a). The decimal numbers is equal to the sum of binary numbers $(b_n)$  times their powers of   $ 2(2^n) .$

That is,

$ b_n \times 2^n + b_{n-1} 2^{n-1}+ ..... + b_02^0 $

$\therefore (1110 \ \ 0100 \ \ 0111 \ \ 1010)_2 $

=  $ (0 \times 2^0) + (1 \times 2^1) + (0 \times 2^2) + (1 \times 2^3) + (1 \times 2^4) + (1 \times 2^5) + (1 \times 2^6)  + ( 0 \times 2^7) + (0 \times 2^8) + (0 \times 2^9) + (1 \times 2^{10} ) $$  + (0 \times 2^{11}) + (0 \times 2^{12}) + (1 \times 2^{13}) + (1 \times 2^{14})+ (1 \times 2^{15})$

= 58490

b).

The left most bit of the number represents the sign of the number. If bit = 1, the number is negative else if the bit is 0, the number is positive.

All the remaining bits (i.e all the bits except the leftmost bit) represent the magnitude of the number.

  Now, X = 1110 0100 0111 1010

  left most bit = 1 => number is negative

  remaining bits Y = 110 0100 0111 1010

  converting Y to decimal => Y = 25722

c).

Check the leftmost bit(lmb) of the number

if leftmost bit is 0 => convert do the binary to decimal conversion

if leftmost bit is 1, follow the following steps

  1. Flip the bits (convert the 0's into 1's and the vice versa)

  2. convert the new number from binary to decimal.

  3. Add a negative sign / multiply by -1

 Now, X = 1110 0100 0111 1010

left most bit = 1;

flipping the bits => Y = 0001 1011 1000 0101

converting Y into decimal => Y = 7045

multiplying Y with -1 => Y = -7045

Therefore, one's complement of X to decimal is -7045

Thus, X = -25722 in decimal.

d).

Check the leftmost bit(lmb) of the number

  if leftmost bit is 0 => convert do the binary to decimal conversion

  if leftmost bit is 1, follow the following steps

  1. Flip the bits (convert the 0's into 1's and the vice versa)

  2. convert the new number from binary to decimal.

  3. Add 1 to the converted number

  4. Add a negative sign / multiply by -1

Now, X = 1110 0100 0111 1010

left most bit = 1;

flipping the bits => Y = 0001 1011 1000 0101

converting Y into decimal => Y = 7045

Adding 1 to Y => Y = 7046

multiplying Y with -1 => Y = -7046

Thus, two's complement of X to decimal is -7046

7 0
3 years ago
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