Answer:
a. This experiment satisfy the conditions below.
b. 0
c. 0
d. 1
e. 0
Step-by-step explanation:
a. This experiment satisfy the following conditions:
1. The experiment consists of n = 1111 identical trials, i.e., to determine if each flight is on-time or not.
2. Each trial results in success or failure, i.e., the flight is on-time or not.
3. The probability of success in each trial is the same, p = 0.8, because a flight is on-time 80% of the time.
4. The trials are independent because the 1111 flights were selected randomly.
5. Te random variable of interest is Y, the number of on-time flights observed in the n = 1111 flights.
b. P(Y = 99) = [tex]\frac{1111!}{99!(1111-99)!}(0.8)^99(0.2)^{1111-99}[/tex] = 0. This is the probability that 99 flights are on time and 1012 are not.
c. P(Y < 99) = [tex]\sum_{i=1}^{98}\frac{1111!}{y!(1111-y)!}(0.8)^y(0.2)^{1111-y}[/tex] = 0. This is the probability that 0 flights are on-time or 1 flight is on-time or ... or 98 flights are on-time.
d. 1 - P(Y < 99) = 1 - 0 = 1. This is the probability that 99 flights are on-time or 100 flights are on-time or ... or all 1111 flights are on-time.
e. [tex]P(77\leq Y \leq 99) = \sum_{i=77}^{99}\frac{1111!}{y!(1111-y)!}(0.8)^y(0.2)^{1111-y}[/tex] = 0 This is the probability that 77 flights are on-time or 78 flights are on-time or ... or 99 flights are on-time.
