Question

The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ. What would the value of σ have to be to ensure that 95% of all readings are within 0.5° of μ?

Answer 1

To ensure that 95% of all temperature readings from a thermocouple are within 0.5° of the actual temperature, the value of the standard deviation (σ) needs to be 0.25°.

Step-by-step explanation:

To ensure that 95% of all temperature readings from a thermocouple are within 0.5° of the actual temperature, the value of the standard deviation (σ) needs to be calculated.

We know that there is a 95% chance that the true population mean value (μ) is between two standard deviations from the sample mean. In this case, we want the interval to be 0.5°, so we can set up the following equation:

2σ = 0.5°

Solving for σ, we get:

σ = 0.5° / 2 = 0.25°

Therefore, the value of σ needs to be 0.25° to ensure that 95% of all temperature readings are within 0.5° of the actual temperature.