Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.

Question

A single thermometer is randomly selected and tested. Let Z represent the reading of this thermometer at freezing. What reading separates the highest 17.34% from the rest? That is, if P(Z>c) = 0.1734, find c.


c=_____ °C

Answer 1

To find the value of \( c \) such that \( P(Z > c) = 0.1734 \), we first need to determine the corresponding z-score for the cumulative probability. This can be done more easily by using the complement:

\[ P(Z \leq c) = 1 - P(Z > c) = 1 - 0.1734 = 0.8266 \]

Now we need to find the z-score that corresponds to a cumulative probability of 0.8266.

Using a standard normal distribution table or a calculator, we look for the z-score that yields an area of 0.8266 to its left. The z-score that corresponds to this cumulative probability is approximately:

\[ z \approx 0.95 \]

Now, we can conclude that:

\[ c \approx 0.95 , °C \]

Thus, the reading that separates the highest 17.34% from the rest is:

\[ c = 0.95 , °C \]