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

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