Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion, ^ p , to be within 0.04 of the true proportion, p (i. e., between 0.16 and 0.24)

Roughly a 95% chance.

Step-by-step explanation:

The standard deviation of sample of size 'n' and with a proportion 'p' is given by:

In this case, in a sample of 400 residents with proportion 20%, the standard deviation is:

The upper and lower limits proposed (0.16 and 0.24) are exactly two standard deviations above and below the mean of 0.20. According to the 95% rule, this interval comprehends 95% of all data. Therefore, there is  roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.

P(0.16 < < 0.24) = 0.9546 or 95.5%

Step-by-step explanation:

We are given that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase.

Let p = % of the residents in a certain state that support an increase in the property tax = 20%

      = % of the residents in a certain state that support an increase in the

            property tax in a sample of 400 residents

The one-sample z sore probability distribution for sample proportion is given by;

         Z = ~ N(0,1)   where, n = sample residents = 400

So, probability that sample proportion will lie between 0.16 and 0.24 is given by = P(0.16 < < 0.24)

 P(0.16 < < 0.24) = P( < 0.24) - P( 0.16)

 P( < 0.24) = P( < ) = P(Z < 1.87) = 0.96926

 P( 0.16) = P( ) = P(Z < -2.18) = 1 - P(Z 2.18)

                                                                 = 1 - 0.98537 = 0.01463

Therefore,  P(0.16 < < 0.24) = 0.96926 - 0.01463 = 0.9546

Hence, it is 95.5% likely that the sample proportion will lie between 0.16 and 0.24.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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