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 1.50 and 2.25 click to view page 1 of the table. click to view page 2 of the table. draw a sketch. choose the correct graph below.

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$. Given $\mu = 0$ and $\sigma=1$.
For $x = 1.50$, $z_1=\frac{1.50 - 0}{1}=1.50$.
For $x = 2.25$, $z_2=\frac{2.25 - 0}{1}=2.25$.

Step2: Use the standard normal table

We want to find $P(1.50From the standard - normal table, $P(Z < 2.25)=0.9878$ and $P(Z < 1.50)=0.9332$.

Step3: Calculate the probability

$P(1.50$P(1.50

Answer:

The probability that the thermometer reading is between $1.50^{\circ}C$ and $2.25^{\circ}C$ is $0.0546$. The correct graph is the one where the area between $z = 1.50$ and $z = 2.25$ under the standard - normal curve is shaded. Without seeing the full - set of options clearly, but conceptually, it should be a graph with a bell - shaped curve (normal distribution curve) and the area between the $z$ - values of $1.50$ and $2.25$ shaded.