Question

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

Explanation:

Step1: Find the probability using the standard normal distribution table

We know that for a standard normal distribution \(Z\sim N(0,1)\), the probability \(P(a < Z < b)=P(Z < b)-P(Z < a)\)
Here \(a = 0.25\) and \(b=1.25\)
From the standard - normal table, \(P(Z < 0.25)=0.5987\) and \(P(Z < 1.25)=0.8944\)

Step2: Calculate the probability

\(P(0.25 < Z < 1.25)=P(Z < 1.25)-P(Z < 0.25)\)
\(P(0.25 < Z < 1.25)=0.8944 - 0.5987\)
\(P(0.25 < Z < 1.25)=0.2957\)

Answer:

The probability of the reading being between \(0.25\) and \(1.25\) is \(0.2957\)