Question 1095022: 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).
B. For a sample of 100 Americans, what is the probability that at least 95 say that they believe texting while driving should be outlawed? Use the normal approximation of the binomial distribution to answer this question (to 4 decimals). Use “Continuity correction factor” method.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! At least 8 is 8, 9, 10
for 8: 10C8*0.97^8*0.03^2=0.0317
for 9: 10C9*0.97^9*0.03=0.2281
for 10, the largest, since the expected value is 9.7, 0.97^10=0.7374
The sum is 0.9972
Check by looking at 7, which must be almost all the rest 10C7*0.97^7+0.03^3=0.0026
=================
np=97, mean
variance is np(1-p)=2.91
sd is sqrt (V)=1.71
Note that n(1-p)=3 and typically that is too small to use the continuity correction factor
For at least 95, use 94.5
z> (94.5-97)/1.71
z > -1.46
p=0.9279
|
|
|
