According to an airline, flights on a certain route are on time 8080% of the time. suppose flights are randomly selected and the number of on-time flights is recorded. (a) explain why this is a binomial experiment. (b) find and interpret the probability that exactly 99 flights are on time. (c) find and interpret the probability that fewer than 99 flights are on time. (d) find and interpret the probability that at least 99 flights are on time. (e) find and interpret the probability that between 77 and 99 flights, inclusive, are on time.

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) = = 0. This is the probability that 99 flights are on time and 1012 are not.

c. P(Y < 99) = = 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. = 0 This is the probability that 77  flights are on-time or 78 flights are on-time or ... or 99 flights are on-time.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3