Question

Lauren is running for president of the student government at UTD. The proportion of voters who favor Lauren is 0.8. A simple random sample of 100 voters is taken. What are the expected value, standard deviation, and shape of the sampling distribution of proportion (, respectively?

Answer 1

Answer:

 $\mu_{x} = 0.8$

   $\sigma  =  0.095  $  

  The shape of this sampling distribution is approximately normal

Step-by-step explanation:

From the question we are told that

  The population proportion is $p = 0.8$

  The sample size is  n = 100

   

Generally the expected value of this sampling distribution is mathematically represented as

          $\mu_{x} = p = 0.8$

Generally the standard deviation of this sampling distribution is mathematically represented as

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

=>  $\sigma  =  \sqrt{ \frac{0.8 (1- 0.8 )}{100 } }$    

=>  $\sigma  =  0.095  $      

Generally given that the sample is  large (i.e  n  >  30 ) and the standard deviation is finite then the shape of this sampling distribution is approximately normal