Question

 According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 15 flights are randomly selected, and the number of on-time flights is recorded.

1. Explain why this is a binomial experiment.

2. Find and interpret the probability that exactly 10 flights are on time.

3. Find and interpret the probability that exactly 8 flights are on time.

4. Find and interpret the probability that exactly 5 flights are on time.

Answer 1

n = 15

p = 0.80

q = 1 - p = 1 - 0.80 =0.20

q = 0.20.

Why this is a binomial experiment....?

If the given experiment is  binomial experiment then it must be satisfied the condition of binomial experiment.

These condition are,

• The experiment are preformed a fixed number of times.
• The trials are independent.
• There are only two possible outcomes of the experiment.
• The probability of success for each trial is constant.

Now checking should this experiment satisfy the binomial experiment condition or not,

• Number of trials are 15 i.e. n=15.
• Trials are independent.
• Possible outcomes are two . i.e. no time or not on time.
• Probability of success is p=0.80 and probability of failure is q=0.20

Here, Given experiment satisfy the condition of binomial experiment.

This is a binomial experiment , because it satisfied the condition of binomial experiment.

1.

Probability that exatly 10 flights are on time is,

10 15-10 P(10) =10 C *p"* 9

P(10) =1. C * 0.8010 * 0.2015-10

P(10) = 3003 * 0.1074 * 0.00032

P(10) = 0.1032

The probability that exactly 10 flights are on time is 0.1032.

2.

Probability that exatly 8 flights are on time is,

15-8 P(8) = C*p** 9

P(8) = C*0.808*0.2015-8

P(8) = 6435 * 0.1678 * 0.0000128

P(8) = 0.01382

The probability that exactly 8 flights are on time is 0.01382

3.

Probability that exatly 5 flights are on time is,

P(5) = C*p* 15-5 9

P(5) = C *0.80*0.2015-5

P(5) = 3003 * 0.3277 * 1.024 * 10-

P(5) = 0.000101

The probability that exactly 5 flights are on time is 0.000101.