Questions: Assume that the readings on the thermometers are normally distributed with a mean of 0°C and standard deviation of 1.00°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to P88, the 88th percentile. This is the temperature reading separating the bottom 88% from the top 12%. Which graph represents P88? Choose the correct graph below. A. B. C. D. The temperature for P88 is approximately °C. (Round to two decimal places as needed.)

Assume that the readings on the thermometers are normally distributed with a mean of 0°C and standard deviation of 1.00°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to P88, the 88th percentile. This is the temperature reading separating the bottom 88% from the top 12%.

Which graph represents P88? Choose the correct graph below.
A.
B.
C.
D.

The temperature for P88 is approximately °C.
(Round to two decimal places as needed.)

Transcript text: Assume that the readings on the thermometers are normally distributed with a mean of $0^{\circ}$ and standard deviation of $1.00^{\circ} \mathrm{C}$. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to $\mathrm{P}_{88}$, the 88th percentile. This is the temperature reading separating the bottom $88\%$ from the top $12\%$. Which graph represents $P_{88}$ ? Choose the correct graph below. A. B. C. D. The temperature for $\mathrm{P}_{88}$ is approximately $\square$ $\square^{\circ}$. (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Identify the Given Information

The problem states that the readings on the thermometers are normally distributed with a mean (μ) of 0°C and a standard deviation (σ) of 1.00°C. We need to find the temperature reading corresponding to the 88th percentile (P88).

Step 2: Understand the Percentile

The 88th percentile (P88) means that 88% of the data falls below this value. In terms of the standard normal distribution, we need to find the z-score that corresponds to the cumulative probability of 0.88.

Step 3: Find the Z-Score

Using a standard normal distribution table or a calculator, we find the z-score that corresponds to a cumulative probability of 0.88. The z-score for 0.88 is approximately 1.175.

Step 4: Convert Z-Score to Temperature

To convert the z-score to the actual temperature, we use the formula: \[ X = \mu + z \cdot \sigma \] Substituting the values: \[ X = 0 + 1.175 \cdot 1.00 \] \[ X = 1.175 \]

Step 5: Choose the Correct Graph

The correct graph should show the area to the left of the z-score 1.175, which represents 88% of the data. This corresponds to graph D.