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patriot [66]
2 years ago
8

Each month Liz pays $35 to her phone company just to use the phone. Each text she sends costs her an additional $0.05. In March

her phone bill was $72.60. In April her phone bill was $65.85. How many texts did she send each
month?
Mathematics
1 answer:
olchik [2.2K]2 years ago
7 0
First let's set up an equation: 35+0.05t. 
35 is the phone rate per month plus the number of texts (t) times 0.05 (cost of 1 text)

Now we can find the amount of texts she sent each month.

March
 35+0.05t=72.60
-35               -35
0.05t=37.60
------   -------
0.05    0.05
t=752

April
 35+0.05t=65.85
-35            -35
0.05t=30.85
------   -------
0.05    0.05
t=617

She sent 752 texts in March and 617 texts in April.


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A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)
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Answer:

a

  The 95% confidence interval is  0.0503  <   p < 0.1297

b

The sample proportion is  \r p =  0.09

c

The critical value is  Z_{\frac{\alpha }{2} } =  1.96

d

 The standard error is  SE   =0.020

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  200

     The number of defective is  k =  18

The null hypothesis is  H_o  :  p  =  0.08

The  alternative hypothesis is  H_a  :  p > 0.08

Generally the sample proportion is mathematically evaluated as

            \r p =  \frac{18}{200}

            \r p =  0.09

Given that the confidence level is  95% then the level  of significance is mathematically evaluated as

        \alpha  =  100 -  95

        \alpha  =  5\%

        \alpha  =  0.05

Next we obtain the critical value of  \frac{ \alpha }{2} from the normal distribution table, the value is  

        Z_{\frac{\alpha }{2} } =  1.96

Generally the standard of error is mathematically represented as

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

substituting values

         SE   =  \sqrt{\frac{0.09  (1 -  0.09)}{200} }

        SE   =0.020

The  margin of error is  

       E =  Z_{\frac{ \alpha }{2} }  * SE

=>    E =  1.96  *  0.020

=>   E =  0.0397

The  95% confidence interval is mathematically represented as

     \r p  -  E  <  \mu <  p <  \r p  + E

=>   0.09 - 0.0397  <  \mu <  p < 0.09 + 0.0397

=>  0.0503  <   p < 0.1297

7 0
2 years ago
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