SOLUTION: A certain company manufactures precision thermometers that are supposed to give readings of 0.00° C at the freezing point of water. Tests on a large sample of these thermometers r
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Question 1192124: A certain company manufactures precision thermometers that are supposed to give readings of 0.00° C at the freezing point of water. Tests on a large sample of these thermometers reveal that some give readings above 0.00° C and some give readings below 0.00° C. Suppose thermometer readings are approximately normally distributed with mean thermometer 0.00° C with a standard deviation of 1.00°. What is the thermometer reading that separates the top 4% of readings from the rest? (Round your answer to two decimal places; add trailing zeros as needed.) Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Use a calculator like this https://davidmlane.com/normal.html
Click "Value from an area"
Input 0.04 as the area
Input 0 as the mean
Input 1 as the standard deviation
Click the "above" option and hit "recalculate" to have 1.751 result.
This means that 4% of the area is to the right of 1.751
If you want to use a table instead of a calculator, then you can use something like this https://www.ztable.net
Locate 0.04 in the table or try to get as close as you can to it.
The value 0.04006 is as close as we can get
Trace to the left until you get to -1.7 at the very left
Trace up the column until you arrive at 0.05 at the very top
Refer to the diagram below.
The headers -1.7 and 0.05 combine to -(1.7+0.05) = -1.75
This shows P(Z < -1.75) = 0.04006 approximately
Due to mirror symmetry, we can say P(Z > 1.75) = 0.04006 approximately
Therefore, we can see that 1.75 is the top 4% cut off point, aka its the value of the 96th percentile since about 96% of the distribution is below z = 1.75
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