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 3.2 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,429 times in a given year. (a) What is the expected number of diversions? (Round your answer to 2 decimal places.) Expected number ___________ (b) What is the approximate normal probability of at least 261 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 approximate normal probability of fewer than 313 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 ______________
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 3.2 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,429 times in a given year.
(a) What is the expected number of diversions? (Round your answer to 2 decimal places.)
Expected number ___________
(b) What is the approximate normal
Probability ______________
(c) What is the approximate normal probability of fewer than 313 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 ______________
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