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5.2 Standard Normal Distribution Notes
Notes
1.) A college dean must select a starting time between 0 and 5 hours, and the
selection is made in such a way that all possible outcomes are equally
likely. If she randomly selects a starting time, what is the probability that
it is during the first half hour or the last half hour?
2.) The Precision Scientific Instrument Company manufactures thermometers
that are supposed to give readings of zero degrees Celsius at freezing
point of water. Tests on large sample of these instruments reveal that at
the freezing point of water, some thermometers give readings below zero
degrees and some above zero degrees. Assume that the mean reading is
zero degrees Celsius and standard deviation of readings is 1.00 degrees
Celsius. Also assume that the readings selected are normally distributed.
If one thermometer is randomly selected, find the probability that, at the
freezing point of water, the reading is between 0 and +1.58 degrees
Celsius.
3.) From the example above, find the probability of randomly selecting one
thermometer that reads between -2.43 degrees and 0 degrees.
***Although a z-score can be negative, the area under the curve can never be
negative.
4.) Once again, make a random selection from the same sample of
thermometers. Find the probability that the chosen thermometer reads (at
freezing point of water) more than +1.27 degrees.
5.) Assuming that one thermometer in our sample is randomly selected, find
the probability that it reads (at freezing point of water) between 1.20
degrees and 2.30 degrees.
Notes
6.) Use the same thermometers as earlier, with temperature readings that are
normally distributed with a mean of 0 degrees Celsius and a standard
deviation of 1.00 degrees Celsius. Find the temperature corresponding to
P95, the 95th percentile. That is, find the temperature separating the
bottom of 95% from the top 5%.
7.) Using the same thermometer, find P10.