Question

In Exercises 6–10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

What is the probability that fewer than three of the five flights arrive on time?

x	P(x)
0	0+
1	0.006
2	0.051
3	0.205
4	0.409
5	0.328

Short answer

The probability that fewer than three of the five flights arrive on time is 0.057.

Step-by-step solution

Given information

The probability distribution for the five American airlines flights is provided.

Compute the probability that fewer than three of the five flights arrive on time

Let X be the number of flights that arrive on time.

Using the probability distribution table, the probability that fewer than three of the five flights arrive on time is computed as,

$$\begin{gathered} P\left(X<3\right)=P\left(X=0\right)+P\left(X=1\right)+P\left(X=2\right) \\ =0+0.006+0.051 \\ =0.057 \end{gathered}$$

Thus, the probability that fewer than three of the five flights arrive on time is 0.057.