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 0.25 and 1.25
draw a sketch. choose the correct graph below.
oa.
ob.
oc.

Explanation:

Step1: Find the probability using the standard normal distribution

The probability \(P(0.25 < Z < 1.25)\) can be found using the property \(P(a < Z < b)=P(Z < b)-P(Z < a)\).
We know that for a standard normal distribution \(Z\sim N(0,1)\), from the standard - normal table:
\(P(Z < 1.25)=0.8944\) and \(P(Z < 0.25)=0.5987\)

Step2: Calculate the difference

\(P(0.25 < Z < 1.25)=P(Z < 1.25)-P(Z < 0.25)\)
Substitute the values:
\(P(0.25 < Z < 1.25)=0.8944 - 0.5987=0.2957\)

Answer:

The probability that the thermometer reading is between \(0.25\) and \(1.25\) is \(0.2957\). For the sketch, option C is correct as it shows the area between \(z = 0.25\) and \(z=1.25\) under the standard - normal curve.