Question

A type of thermometer has temperature readings at the freezing point of water that are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. Find the temperature corresponding to P23, the 23rd percentile.

a) 0.9893°C
b) 0.23°C
c) -0.74°C
d) -2.849°C

Answer 1

The temperature corresponding to the 23rd percentile for a thermometer with readings normally distributed around the freezing point of water (0°C) with a standard deviation of 1.00°C is -0.74°C. This is calculated using the Z-score corresponding to the 23rd percentile.

Step-by-step explanation:

To find the temperature corresponding to the 23rd percentile (P23) in a normally distributed data set with a mean of 0°C and a standard deviation of 1.00°C, we need to use a Z-score table or a calculator that can determine the Z-score associated with a given percentile.

Looking up the 23rd percentile on a Z-score table, or using a calculator, we find that the Z-score corresponding to the 23rd percentile is approximately -0.74. Therefore, to find the actual temperature, we apply the following formula where Z is the Z-score, μ is the mean, and σ is the standard deviation:

Temperature = μ + Z × σ

Plugging in the values we get:

Temperature = 0°C + (-0.74) × 1.00°C

Temperature = -0.74°C

Therefore, the correct answer is c) -0.74°C, which is the temperature corresponding to the 23rd percentile.