Answer to Question #111847 in Statistics and Probability for Cec

Question

What is the probability that no more than 156 U.S adults of the 240 surveyed believe solar energy is very effective in minimizing air pollution?

Answer 1

$Let\;p=\frac{156}{240}=0.65\\ np=0.65\times 240=156, \\n(1-p)=0.35\times 240=84,\\ np\geq 5, n(1-p)\geq5, \\ \text{so we can use the Normal Distribution}\\ \text{ to Approximate Binomial Probabilities} \\p(x \leq 156)=p(z \leq \frac {156.5-240\times 0.65}{\sqrt{240(0.65)(0.35)}})\\ p(z \leq 0.07)=0.5+p(0\leq z\leq 0.07)\\ =0.5+0.0279=0.5279$