According to an airline, flights on a certain route are on time 80% of the time.

Question

According to an airline, flights on a certain route are on time 80% of the time. Suppose 10 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance.

(a) Determine whether this is a binomial experiment.

(b) Find and interpret the probability that exactly 8 flights are on time.

(c) Find and interpret the probability that at least 8 flights are on time.

(d) Find and interpret the probability that fewer than 8 flights are on time.

(e) Find and interpret the probability that between 6 and 8 flights, inclusive, are on time.

Explanation / Answer

Solution:-

p = 80/100 = 0.80

n = 10

(a) Yes this is binomial experiment.

The experiment consists of n repeated trials.

Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.

The probability of success, denoted by P, is the same on every trial.

The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

(b) The probability that exactly 8 flights are on time is 0.302.

x = 8

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 8) = 0.302

(c) The probability that at least 8 flights are on time is 0.678.

x = 8

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 8) = 0.678

(d) The probability that fewer than 8 flights are on time is 0.322.

x < 8

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 8) = 0.322

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