According to an airline, flights on a certain route are on time 85% of the time.

Question

According to an airline, flights on a certain route are on time 85% of the time. Suppose 25 flights are randomly selected and the number of on time flights is recorded.

a) Determine whether this is a binomial experiment and explain why

c) Find and interpret the probability that exactly 18 flights are on time

d) Find and interpret the probability that at least 18 flights are on time

e) Find and interpret the probability that fewer than 18 flights are on time

f) Find and interpret the probability that between 16 and 18 flights, inclusive, are on time.

(Round all answers to four decimal places), thank you in advance

Explanation / Answer

a. The binomial distribution describes the behavior of a count variable X if the following conditions apply:

1: The number of observations n is fixed. Here it is 25

2: Each observation is independent. Yes they are independent

3: Each observation represents one of two outcomes ("success" or "failure"). One time or not on time

4: The probability of "success" p is the same for each outcome.Here it is 0.85

As all the conditions are satisfied this is binomial distribution

c. P(x=18)=25c18*(0.85)^18*(1-0.85)^7=0.0441

d. P(x>=18)=P(x=18+19....25)=0.9745

e. P(x<18)=P(x=0,1,....17)=0.0255

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.