The binomial probability distribution for the number of viewers watching 60 Minutes among 10 randomly selected TV viewers
Assume that viewers are randomly selected from a population in which 20% of the viewers are watching 60 Minutes.
n = 10
p = 0.20
x = number of 60 Minutes viewers
5-3 page 214 number 29 (link to answer)Assume that viewers are randomly selected from a population in which 20% of the viewers are watching 60 Minutes.
n = 10
p = 0.20
x = number of 60 Minutes viewers
Fill out the table to the right, then answer the questions.
Find the binomial probability distribution for 10 randomly selected TV viewers watching 60 Minutes if the probability that any one of them watching 60 Minutes is 20%
Use Table A-1 page 610 to fill out the table for n = 10 and p = 0.200
a. Find the probability that no viewers are watching 60 Minutes
b. Find the probability that at least 1 viewer is watching 60 Minutes
0.003 + 0.001 = 0.4%
10.7% is the probability that no viewers are watching 60 Minutes.
10.7% is the probability that no viewers are watching 60 Minutes.
"At least 1 viewer" is equivalent to "1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 viewers". Sum the probabilities of 1 to 10 viewers to get a probability of 89.3% that at least 1 viewer is watching 60 Minutes.
c. Find the probability that at most 1 viewer is watching 60 Minutes
"At most 1 viewer" is equivalent to "0 or 1 viewer". Sum the probabilities of 0 and 1 viewer to get a probability of 37.5% that at most 1 viewer is watching 60 Minutes.
d. Is the answer to "at most 1" sensible or does it seem too large?
The most likely result is 2 of 10 viewers are watching 60 Minutes. In fact 0, 1, 2, 3, or 4 viewers of <span class="italics"><span class="italics">60 Minutes</span></span> out of 10 is usual or greater than 5%. Thus is is hardly surprising that the probability of "0 or 1" viewer is large.