Question

assume that thermometer readings are normally distributed with a mean of ( 0^{circ} mathrm{c} ) and a standard deviation of ( 1.00^{circ} mathrm{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.
ob.
oc.

Explanation:

Step1: Determine the correct graph

We need to find the graph that represents the area between \(z = 0.50\) and \(z=1.75\). The standard normal distribution is symmetric about \(z = 0\). The area between two positive \(z\)-scores should be a region that is bounded on the left by \(z = 0.50\) and on the right by \(z = 1.75\).

• Option A: The shaded region does not represent the area between \(z = 0.50\) and \(z = 1.75\) correctly as it seems to have an incorrect lower - bound interpretation.
• Option B: The \(z\)-scores are in the wrong order. Since \(0.50<1.75\) for a standard normal distribution (where larger \(z\)-scores are to the right of smaller positive \(z\)-scores), this option is incorrect.
• Option C: This graph correctly represents the area between \(z = 0.50\) (left - hand side of the shaded region) and \(z = 1.75\) (right - hand side of the shaded region)

Answer:

C.