Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239
Instructor: Shawn Parvini - 16 weeks Date: 3/18/10 Book: Triola: Elementary Statistics, 11e
Time: 4:05 PM Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of
1.00 °C. If 3.5% of the thermometers are rejected because they have readings that are too high and another 3.5% are
rejected because they have readings that are too low, ﬁnd the two readings that are cutoff values separating the rejected
thermometers from the others. First, draw a bell-shaped curve and identify the region under the curve that corresponds to the given probability. If that region is not a cumulative region from the left, work instead with a known region that is a cumulative region from the
leﬁ. The graph below represents the region in which thermometers are rejected. Y The two values must be approached individually. First, consider the value for the lower 3.5%. Using the cumulative area
from the left, locate the closest probability in the body of a table of normal distribution values and identify the z score
corresponding to 0.035. Alternately, technology may be used to determine the most accurate 2 score. The z score for the lower 3.5% is approximately - 1.81. The value for the upper 3.5% must ﬁrst be reevaluated as a known region that is a cumulative region from the left.
Instead of ﬁnding the z score where the area to the right is 0.035, ﬁnd the z score where the area to the left is
1 - 0.035 = 0.965. Now, ﬁnd the z score corresponding to 0.965 either on a normal distribution table or by using technology. 2:51.81 Therefore, the cutoff values are approximately — 131° and l.81°. Page 1 ...
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- Spring '10