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alukav5142 [94]
3 years ago
13

Write these numbers in standard notation. 3.05 x 10–3 8.92 x 106

Mathematics
2 answers:
Bad White [126]3 years ago
3 0

3.05  \times   {10}^{ - 3} =0.00305 \\8.92 \times  {10}^{6} =   8920000
Flauer [41]3 years ago
3 0

Answer:

We have been given the two numbers:

3.05 \cdot 10^{-3}

And 8.92\cdot 10^{6}

x^{-a}=\frac{1}{x^a}

10^{-3}=\frac{1}{10^3}=\frac{1}{1000}

So, 3.05 \cdot 10^{-3}=\frac{3.05}{1000}

\Rightarrow 0.00305

And 8.92\cdot 10^{6}=\frac{892}{100}\cdot {1000000}

892\cdot 10000

\Rightarrow 8920000

3.05 \cdot 10^{-3}=0.00305

8.92\cdot 10^{6}=8920000

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A random sample of 300 circuits generated 13 defectives. Use the data to test the hypothesis Upper H Subscript 0 Baseline colon
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Complete Question

A random sample of 300 circuits generated 13 defectives. a. Use the data to test

                            H_o : p = 0.05

Versus

 

                          H_1 : p \ne 0.05

Use α = 0.05. Find the P-value for the test

   

Answer:

The  p-value is  p-value =  0.5949        

Step-by-step explanation:

From the question we are told that

  The sample size is  n = 300

    The number of defective circuits is  k = 13

Generally the sample proportion of defective circuits is mathematically represented as

        \^ p = \frac{k}{n}

=>     \^ p = \frac{13}{300}

=>     \^ p = 0.0433

Generally the standard Error is mathematically represented as

       SE  = \sqrt{\frac{p(1- p)}{n} }

=>     SE  = \sqrt{\frac{0.05(1- 0.05)}{300} }

=>     SE  = 0.0126

Generally the test statistics is mathematically represented as

       z =  \frac{\^ p - p }{SE}

=>     z =  \frac{0.0433 - 0.05 }{0.0126}

=>     z =  -0.5317

From the z table  the area under the normal curve to the left  corresponding to  -0.5317  is

         (P < -0.5317 ) = 0.29747

Generally the p-value is mathematically represented as

       p-value =  2 * P(Z <  -0.5317 )

=>     p-value =  2 * 0.29747

=>     p-value =  0.5949        

     

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