An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 135 lb and a standard deviation of 34.4 lb. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 181 lb. The probability is approximately 0.46950.4695. (Round to four decimal places as needed.) b. If 40 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 181 lb. The probability is approximately 5.43915.4391. (Round to four decimal places as needed.)
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!
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