One way of checking the effect of undercoverage, nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 12% of American adults identify themselves as black. Suppose we take an SRS of 1500 American adults and let X be the number of blacks in the sample. Use a Normal distribution to estimate the probability that the sample will contain between 165 and 195 blacks.

Solution :

Given :

p = 12% = 0.12

n = 15..

Mean is defined as the product of a sample size n and the probability p such that :

             = 180

Standard deviation may be defined as the square of a product of the sample size n, the probability p and the probability 1-p :

     ≈  12.5857

The z-score is given by :

 ≈  -1.19  

 ≈  1.19  

Now determining the corresponding probability using table  :

P (165 ≤ X ≤ 195 ) = P (-1.19 ≤ Z ≤ 1.19 )

                            = 1-2 x P(Z < -1.19)

                            = 1-2 x 0.1170

                            = 1-0.2340

                            = 0.7660

                             = 76.60%

step-by-step explanation:

first, eliminate the parenthesis:

3

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second, group like terms:

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third, combine like terms:

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3

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answer: the first graph

step-by-step explanation: