When confronted with an in-flight medical emergency, pilots and crew can consult

Question

When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 3.8 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,455 times in a given year (a)What is the expected number of diversions? (Round your answer to 2 decimal places.) Expected number 17.58 (b)What is the probability of at least 317 diversions (Round your standard deviation value to 4 decimal places and your z-value to 2 decimal places. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.) Probability (c)What is the probability of fewer than 363 diversions? (Round your standard deviation value to 4 decimal places and your z-value to 2 decimal places. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimal places.) Probability

Explanation / Answer

Ans:

a)Expected number of diversions=8455*0.038=321.29

b)Normal approximation

mean=321.29

std.dev=sqrt(8455*0.038*0.962)=17.5807

z=(317-321.29)/17.5807=-0.24

P(z>=-0.24)=0.5948

c)

z=(363-321.29)/17.5807=2.37

P(z<2.37)=0.9911

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