Assume the readings on thermometers are normally distributed

Assume the readings on thermometers are normally distributed with a mean of

0degrees°C

and a standard deviation of

1.00degrees°C.

Find the probability that a randomly selected thermometer reads between

negative 1.061.06

and

negative 0.280.28

and draw a sketch of the region.Click to view page 1 of the table.

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Click to view page 2 of the table.

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Sketch the region. Choose the correct graph below.

A.

-0.28-1.06

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the left side. Moving from left to right, the regions left of the second line are shaded. The z-axis below this line is labeled negative 0.28. The z-axis below the first line is labeled negative 1.06.

B.

-0.28-1.06

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the left side. The region between the 2 lines is shaded. Moving from left to right, the z-axis below the first line is labeled negative 1.06. The z-axis below the second line is labeled negative 0.28.

C.

-0.28-1.06

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the left side. Moving from left to right, the region left of the first line is shaded. The z-axis below this line is labeled negative 1.06. The z-axis below the second line is labeled negative 0.28.The probability is

nothing.

(Round to four decimal places as needed.)

Solution

a)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    -1.06      
x2 = upper bound =    -0.28      
u = mean =    0      
          
s = standard deviation =    1      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.06      
z2 = upper z score = (x2 - u) / s =    -0.28      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.1446  
P(z < z2) =    0.3897
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.2451 [ANSWER]

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B.

-0.28-1.06

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the left side. The region between the 2 lines is shaded. Moving from left to right, the z-axis below the first line is labeled negative 1.06. The z-axis below the second line is labeled negative 0.28. [ANSWER, OPTION B]