Question

assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°c. a thermometer is randomly selected and tested. draw a sketch and find the temperature - reading corresponding to p97, the 97th percentile. this is the temperature reading separating the bottom 97% from the top 3%. click to view page 1 of the table. click to view page 2 of the table. which graph represents p97? choose the correct graph below

Explanation:

Step1: Recall the concept of percentile in normal - distribution

The 97th percentile $P_{97}$ means that 97% of the data lies to the left of the value. In a standard normal distribution $Z\sim N(0,1)$, we use the standard - normal table (z - table) to find the z - score corresponding to the cumulative probability of 0.97.

Step2: Look up the z - score in the z - table

Looking up the value in the standard - normal table, the z - score corresponding to a cumulative probability of 0.97 is approximately $z = 1.88$.

Step3: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the original normal distribution. Given $\mu = 0$ and $\sigma=1$, we substitute the values into the formula: $1.88=\frac{x - 0}{1}$.

Step4: Solve for $x$

From $1.88=\frac{x - 0}{1}$, we can directly get $x=1.88$.

For the graph of $P_{97}$:
The normal distribution is symmetric about the mean $\mu = 0$. The 97th percentile is a value on the right - hand side of the mean (since 97% of the data is to the left of it). The graph should have the shaded area (representing the cumulative probability of 0.97) to the left of a value on the positive x - axis.

Answer:

The temperature reading corresponding to $P_{97}$ is $1.88^{\circ}C$. The correct graph is the one with the shaded area to the left of a positive x - value (assuming the x - axis represents temperature and the y - axis represents the probability density function of the normal distribution). Without seeing the exact details of the graphs A, B, C, and D, the correct graph is the one where the shaded region is on the left - hand side of a positive x - value and represents 97% of the area under the curve.