Assume that the reading on the thermometers are normally distributed with a mean
ID: 3153020 • Letter: A
Question
Assume that the reading on the thermometers are normally distributed with a mean of 0degree and standard deviation of 1.00degree C. Assume 2.1% of the thermometer, are rejected because they have readings that are too high and another 2.1% are rejected because they they have reading that are too low. Draw a sketch and find the two leadings that are cutoff values separating the rejected thermometers from the others. Which graph represents the region in which thermometers are rejected? C hoove the correct graph below. The cutoff values are square degrees. (Use a comma to separate answers as needed. Round to two decimal places as needed.)Explanation / Answer
1.
The correct graph have cutoffs on both ends, and the shaded area are the oiter values.
hence,
OPTION C [CORRECT GRAPH]
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2.
Lower cutoff:
First, we get the z score from the given left tailed area. As
Left tailed area = 0.021
Then, using table or technology,
z = -2.03
As x = u + z * s,
where
u = mean = 0
z = the critical z score = -2.03
s = standard deviation = 1
Then
x = critical value = -2.03
upper cutoff:
First, we get the z score from the given left tailed area. As
Left tailed area = 0.979
Then, using table or technology,
z = 2.03
As x = u + z * s,
where
u = mean = 0
z = the critical z score = 2.03
s = standard deviation = 1
Then
x = critical value = 2.03
Hence, the critical values are
x = -2.03, 2.03 [ANSWER]
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