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fgiga [73]
4 years ago
10

A and B are two events.

Mathematics
1 answer:
svlad2 [7]4 years ago
5 0

Answer:

A and B are not independent events because P(A|B)≠P(A)

is the correct answer.

Step-by-step explanation:

If A and B are independent then we must have

P(AB) = P(A) P(B) and also

P(A/B) = P(A)

We are given that

A and B are two events.

Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .

P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3

i.e. P(A/B) is not equal P(A)

Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)

Hence A and B are not independent.


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The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we w
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Answer:

The sample size is  n  = 600

Step-by-step explanation:

From the question we are told that

    The  sample proportion is  \r  p = 0.48

     The  margin of error is  MOE  =  0.04

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

        \alpha  =  100 - 95

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        \alpha  =  0.05

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

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

The reason we are obtaining critical value of    \frac{\alpha }{2} instead of    \alpha is because  

\alpha represents the area under the normal curve where the confidence level interval (  1-\alpha) did not cover which include both the left and right tail while  

\frac{\alpha }{2} is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

      MOE  =  Z_{\frac{\alpha }{2} } *  \sqrt{ \frac{\r p(1-  \r p )}{n} }

substituting values

          0.04= 1.96*  \sqrt{ \frac{0.48(1-  0.48 )}{n} }

         0.02041 = \sqrt{ \frac{0.48(52 )}{n} }

         0.02041 = \sqrt{ \frac{ 0.2496}{n} }

          0.02041^2  = \frac{ 0.2496}{n}

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5 0
3 years ago
PLEASE HELP ASAP!!!
barxatty [35]

Answers:

  • <u>24000 dollars</u> invested at 4%
  • <u>18000 dollars</u> was invested at 7%

======================================================

Work Shown:

x = amount invested at 4%

If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%

She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account

This means we have

0.04x+0.07(42000-x)

0.04x+0.07*42000-0.07x

0.04x+2940-0.07x

-0.03x+2940

This represents the total amount of money earned after 1 year.

We're told the amount earned in interest is $2220, so we can say,

-0.03x+2940 = 2220

-0.03x = 2220-2940

-0.03x = -720

x = -720/(-0.03)

x = 24000 dollars is the amount invested at 4%

42000-x = 42000-24000 = 18000 dollars was invested at 7%

----------------------

As a check, we can see that

18000+24000 = 42000

and also

0.04x = 0.04*24000 = 960 earned from the first account

0.07*18000 = 1260 earned from the second account

1260+960 = 2220 is the total interest earned from both accounts combined

This confirms our answers.

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