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Question:

If the standard deviation for lifetimes of vacuum cleaners is estimated to be 400 hours, how large a sample?

must be taken in order to be 90% confident that the margin of error will not exceed 50 hours? Please show work

Answer:

The 90% confidence z-value from the normal probability table is 1.645 Sample size n = [ (1.645) SD /error] ^2 n = {(1.645)(400)/50]^2 n =173.18 ≈ 174

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