Assume the readings on thermometers are normally distributed

Assume the readings on thermometers are normally distributed with a mean of 0 degree C and a standard deviation of 1.00 degree C. Find the probability that a randomly selected thermometer reads between -2.27 and -0.87 and draw a sketch of the region. Sketch the region. Choose the correct graph below. The probability is

Solution

As the mean is 0 C, then both values -2.27 and -0.87 are to the left of the mean (peak).

Thus, the area is between those two values, so it is

OPTION B [CORRECT FIGURE]

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z1 = lower z score =    -2.27      
z2 = upper z score =     -0.87      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.0116      
P(z < z2) =    0.1922      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.1806 [ANSWER]