Question

assume that thermometer readings are normally distributed with a mean of 0°c and a standard deviation of 1.00°c. a thermometer is randomly selected and tested. for the case below, draw a sketch, and find the probability of the reading. (the given values are in celsius degrees.)
between 0.50 and 1.75
click to view page 1 of the table. click to view page 2 of the table.
draw a sketch. choose the correct graph below.
oa.
z=0.50
z=1.75
ob.
z=0.50
z=1.75
oc.
z=0.50
z=1.75

Explanation:

Step1: Recall the properties of the standard normal distribution

The standard normal distribution is symmetric about \(z = 0\). The area between two \(z\)-scores \(z_1\) and \(z_2\) (\(z_1

Step2: Use the standard normal table

From the standard normal table:

• \(\Phi(0.50)\) (the area to the left of \(z = 0.50\)) is \(0.6915\)
• \(\Phi(1.75)\) (the area to the left of \(z = 1.75\)) is \(0.9599\)

Step3: Calculate the probability

\(P(0.50 < Z<1.75)=\Phi(1.75)-\Phi(0.50)\)

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Answer:

The probability that the reading is between \(0.50\) and \(1.75\) is \(0.2684\)