Question

A CBS News/New York Times survey found that 97% of Americans believe that texting while driving should be outlawed (CBS News website, January 5, 2015). a. For a sample of 10 Americans, what is the probability that at least 8 say that they believe texting while driving should be outlawed? Use the binomial distribution probability function to answer this question (to 4 decimals).

Answer 1

Answer: 0.9972

Step-by-step explanation:

Given : The proportion of Americans believe that texting while driving should be outlawed : p= 0.97

Sample size : n= 10

Using Binomial distribution , the probability of getting success in x trials is given by:-

$P(x)=^nC_xp^x(1-p)^{n-x}$, where p is probability of success in each trial and n is sample size.

Then, the probability that at least 8 say that they believe texting while driving should be outlawed will be :_

$P(x\geq8)=P(8)+P(9)+P(10)\\\\=^{10}C_{8}(0.97)^8(0.03)^2+^{10}C_{9}(0.97)^9(0.03)^1+^{10}C_{10}(0.97)^{10}(0.03)^0\\\\=\dfrac{10!}{8!2!}(0.97)^8(0.03)^2+(10)(0.97)^{9}(0.03)+(0.97)^{10}\ \ \because\ ^nC_{n-1}=n\ \&\ ^nC_{n}=1\\\\=0.997235050549\approx0.9972$

Hence, the required probability = 0.9972