An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb. and 211 lb. The new populations of pilots has normally distributed weights with a mean of 150 lbs. and a standard deviation of 34.4 lbs.
a. If a pilot is randomly selected, find the probability that his weight is between 150 lb. and 211 lb. The probability is approximately?
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Okay, if the mean is 150 lbs and the std dev is 34.4 pounds, 68.2% of the pilots will have a weight within 1 std dev, or in the range 150-34.4= 115.6 to 150+34.4 = 184.4
95.45% will have a weight within 2 std deviation, or the range 150-2*34.4 = 81.2 to 150+2*34.4=218.8
With a normal distribution, the population is equally balanced on each side of the mean, so we can take half of those percentages to get the section between 150 (the mean) and 211. Therefore, about 47% or so should fall within 150 and 211, or P = 0.47.
Some of the lighter pilots may want to put on lead underwear :-)
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Hmm. Well, I wonder how exact they want it to be? 95.45/2 = 47.725, but that goes out to slightly beyond 211 pounds. Central Limit Theorem is what allows us to use the 68.2/95.45/97.3 rule of thumb about the distribution around the mean. In any case, I'm sorry that you got that marked wrong, and am curious what the correct answer is supposed to be.
on the previous ones ive had to do, it is asking for the cumulative area from the left
okay, but here we are only interested in the area from the mean, to the mean+2 sigma.
ok so it gave me the right answer of .5224 but not sure how they did that
well, 1-0.5224 = 0.4776 or 47.76%. I don't see how they are getting > 0.5, however!