SOLUTION: Assume that at an actual temperature of freezing (0°C) on a batch of thermometers, the temperatures displayed are normally distributed with a mean of 0°C and a standard deviation
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Question 1196866: Assume that at an actual temperature of freezing (0°C) on a batch of thermometers, the temperatures displayed are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than
0.76°C if the actual temperature is freezing (0°C).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 0
standard deviation is 1
z-score = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
fox x = .76, the formula becomes z = (.76 - 0) / 1 = .76
area to the left of a z-score of .76 = .77637.
this means that the probability of obtaining a reading less than .76 from a randomly selected thermometer = .77637 = 77.637%.
this means that 77.637% of the thermometers in the batch of thermometers will have a reading less than .76 degrees centigrade when the actual temperature is 0 degrees centigrade.
on the graph, the normal distribution will look like this:
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