## Related questions with answers

When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at MedAire, an emergency facility in Tempe, Arizona. If MedAire is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing.

(a) If MedAire is called 8,465 times (as it was in 2002), what is the expected number of diversions?

(b) What is the probability of at least 400 diversions?

(c) Fewer than 450 diversions? Show your work carefully. (Data are from Popular Science 263, no. 5 [November 2003], p. 70.)

Solution

Verified**a.** In this exercise, we are given that there is a $4.8\%$ chance that a certain flight will be diverted for an immediate landing if the pilots and crew will call MedAire during an in-flight emergency. Now, we will calculate the expected number of diversions if MedAire is called $8,465$ times.

*Given the number of observations $(n)$ and the probability of success $(\pi)$, how can we calculate the binomial distribution's mean and standard deviation?*

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