Assume the readings on thermometers are normally distributed with a mean of 0°C
ID: 3155687 • Letter: A
Question
Assume the readings on thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the probability that a randomly selected thermometer reads between 2.08 and 1.39 and draw a sketch of the region. Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING... Sketch the region. Choose the correct graph below. A. -1.39 -2.08 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 2.08. The z-axis below the second line is labeled negative 1.39. B. -1.39 -2.08 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 2.08. The z-axis below the second line is labeled negative 1.39. C. -1.39 -2.08 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 1.39. The z-axis below the first line is labeled negative 2.08. The probability is (Round to four decimal places as needed.)
Explanation / Answer
The standard normal variate Z = (x - µ) /
A. Here µ = 0 , = 1, x1 = -2.08, x2 = -1.39
So, z1 = (-2.08 - 0) / 1 = -2.08 and z2 = (-1.39 - 0) / 1 = -1.39
So P( -2.08 < z < -1.39 ) = P( 1.39 < Z < 2.08) Since it is a symmetric curve, the area between the limit - to 0 = 0 to + = 0.5
So P(1.39<Z<2.08) = P(0<Z<2.08) - P(0<Z<1.39) = 0.4812 - 0.4177 = 0.0635.
B & C already explianed