Assume the readings on thermometers are normally distributed with a mean of 0deg
ID: 3183690 • Letter: A
Question
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 2.052.05
and
negative 0.040.04
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.
-0.04-2.05
Edit Coordinates... (0,0)
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 2.05. The z-axis below the second line is labeled negative 0.04.
B.
-0.04-2.05
Edit Coordinates... (0,0)
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 0.04. The z-axis below the first line is labeled negative 2.05.
C.
-0.04-2.05
Explanation / Answer
Mean ( u ) =0
Standard Deviation ( sd )=1
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < -2.05) = (-2.05-0)/1
= -2.05/1 = -2.05
= P ( Z <-2.05) From Standard Normal Table
= 0.02018
P(X < -0.04) = (-0.04-0)/1
= -0.04/1 = -0.04
= P ( Z <-0.04) From Standard Normal Table
= 0.48405
P(-2.05 < X < -0.04) = 0.48405-0.02018 = 0.4639
b.
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 2.05. The z-axis below the second line is labeled negative 0.04.