Question
Suppose that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C.
If 8% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
If 8% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
Answers
Draw a sketch of what you want, similar to this:
http://prntscr.com/8kitsp
THen look up the standard normal distribution table (left tail) the number of standard deviations that correspond to 92%. (it should be between 1.4 and 1.5).
Since each standard deviation corresponds to 1°, so you can figure out the cut-off temperature.
http://prntscr.com/8kitsp
THen look up the standard normal distribution table (left tail) the number of standard deviations that correspond to 92%. (it should be between 1.4 and 1.5).
Since each standard deviation corresponds to 1°, so you can figure out the cut-off temperature.
or, you can play around with Z values and areas at
http://davidmlane.com/hyperstat/z_table.html
http://davidmlane.com/hyperstat/z_table.html
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