Answer:
a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.
b) P(X < 4) = 0.4576
c) P(X=6) + P(X=7) = 0.1064
d) Mean = 3.69
Step-by-step explanation:
a) The population parameter stated in the survey is the event that represents a success. Hence, A success is an adult who enjoyed the commercials more than the event on TV itself.
b) The probability that less than four people enjoyed the commercials more than the event
This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of adults sampled = 9
x = Number of successes required = number of people that enjoyed the commercial more than the event on TV = less than 4
p = probability of success = probability of enjoying the commercial more than the event = 0.41
q = probability of failure = probability of NOT enjoying the commercial more than the event = 1 - 0.41 = 0.59
P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.00866299582 + 0.05418043148 + 0.15060323326 + 0.24419846296
P(X < 4) = 0.45764512351 = 0.4576
c) The probability that exactly six or seven people enjoyed the commercials more than the event = P(X=6) + P(X=7)
Using the Binomial distribution formula
P(X=6) + P(X=7) = 0.08194801935 + 0.02440582659 = 0.106353846 = 0.1064
d) Mean = expected value of people that would enjoy the commercial more than the main event = np = 9×0.41 = 3.69
Hope this Helps!!!