Question

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. A single thermometer is randomly selected and tested. Find P59, the 59-percentile. Round to 3 decimal places. This is the temperature reading separating the bottom 59% from the top 41%.

P59 = °C

Answer 1

Solution: 59-percentile is 0.228°C

Given information,

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.

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.59. Mathematically, x is such that:

P(X<=x)=0.59

The corresponding z score score so that the cumulative standard normal probability distribution is 0.59 is Zc​=0.2275

x= μ+zc​×σ =0+0.2275×1=0.2275