Questions: Assume that the freezing point for water is normally distributed and has a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. What temperature reading separates the top 10% from the others? Use [Select] to find the answer, which is [Select]

Solution Steps

To find the temperature reading that separates the top 10% from the others in a normally distributed dataset, we need to determine the 90th percentile of the distribution. This can be done using the inverse of the cumulative distribution function (CDF) for a normal distribution, often referred to as the percent-point function (PPF).

We need to find the temperature reading that separates the top 10% of a normally distributed dataset with a mean of 0°C and a standard deviation of 1°C. This is equivalent to finding the 90th percentile of the distribution.

The 90th percentile of a normal distribution can be found using the percent-point function (PPF), which is the inverse of the cumulative distribution function (CDF). For a normal distribution with mean \(\mu = 0\) and standard deviation \(\sigma = 1\), the 90th percentile is calculated as follows:

\[ x = \mu + \sigma \cdot z \]

where \(z\) is the z-score corresponding to the 90th percentile.

Using the PPF, we find that the z-score for the 90th percentile is approximately 1.2816. Therefore, the temperature reading is:

\[ x = 0 + 1 \cdot 1.2816 = 1.2816 \]

Final Answer