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Problem:
Mechanical measurements on supposedly identical objects usually vary. The variation often follows a Normal distribution. The stress required to break a type of bolt varies Normally with mean 75 kilopounds per square inch (ksi) and standard deviation 8.3 ksi.
Required:
(i) What percent of these bolts will withstand a stress of 90 ksi without breaking?
(ii) What range covers the middle 50% of breaking strengths for these bolts?
This situation comes up especially when the Xi are [copies of] the same space, such as R with its usual topology. Then ITi Xi is the set of all functions from I into R, often called RI .)
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