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 p93, the 93rd percentile. this is the temperature reading separating the bottom 93% from the top 7%. click to view page 1 of the table. click to view page 2 of the table. which graph represents p93? choose the correct graph below.

Explanation:

Step1: Recall the definition of percentile

The $93$rd percentile $P_{93}$ means that $93\%$ of the data lies to the left of the value corresponding to $P_{93}$ under the normal - distribution curve.

Step2: Analyze the normal - distribution graph

In a normal - distribution graph (bell - shaped curve) with mean $\mu = 0$ and standard deviation $\sigma=1$, the area under the curve represents probabilities. The $93$rd percentile will have the area to the left of the value equal to $0.93$.

Answer:

The graph that has the shaded area to the left of a value on the x - axis equal to $0.93$ is the correct representation of $P_{93}$. Without seeing the actual options clearly (since the image of the options is not fully legible in text form), the correct graph should have a large portion (93%) of the area under the normal curve shaded to the left of a particular x - value. If we assume a standard normal distribution $Z\sim N(0,1)$, we can use the standard normal table (z - table) to find the z - score corresponding to an area of $0.93$. Looking up in the z - table, the z - score corresponding to an area of approximately $0.93$ is around $z = 1.48$. The graph should show a normal curve centered at $0$ with the area to the left of $z = 1.48$ shaded.