Question

Delta airline flights from Orlando to Chicago are on time 70% of the time suppose 6 fights are randomly selected and the number on time flight is recorded determine the following probability around solution to 4 decimal places the probability that exactly 4 flights our own time is

Answer 1

The flight is either early or late. Since these are the only outcomes, this is a binomial probability. The formula for determining binomial probability is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n = number of trials

x = number of successes

p = probability of success

q = probability of failure

The success in this case is the outcome of the flight being on time. Thus, we have

n = 6

p = 70/100 = 0.7

q = 1 - p = 1 - 0.7 = 0.3

For the probability that exactly 4 flights our own time is on time,

x = 4

Thus

P(x = 4) = 6C4 * 0.7^4 * 0.3^(6 - 4)

P(x = 4) = 0.3241

From the binomial distribution calculator, the probability of at most 3 flights is

`P(x\leq3)\text{ = 0.2557}`

From the binomial distribution calculator, the probability of at least 5 flights is

`P(x\ge5)\text{ = 0.4202}`