Respuesta :
Answer:
Probability that the potential candidate will run for President election is 0.0096.
Step-by-step explanation:
We are given that a potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy.
To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy.
Let p = % of Americans voice support for her candidacy
The z score probability distribution for sample proportion is given by;
                Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex]  ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans support her candidacy = 35%
      n = sample of Americans = 500
Now, probability that the potential candidate will obtain a p^ ≥ 0.30 and run for President is given by = P( [tex]\hat p[/tex] ≥ 0.30)
   P( [tex]\hat p[/tex] ≥ 0.30) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ≥ [tex]\frac{0.35-0.30}{\sqrt{\frac{0.35(1-0.35)}{500}} }[/tex] ) = P(Z ≥ 2.34) = 1 - P(Z [tex]\leq[/tex] 2.34)
                                   = 1 - 0.9904 = 0.0096
The above probability is calculated by looking at the value of x = 2.34 in the z table which has an area of 0.9904.
Hence, the required probability is 0.0096.
