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 0.6° of μ?

Answer 1

Answer: 0.3061.

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean $\mu$, the actual temperature of the medium, and standard deviation $\sigma$.

Let X be the random variable that represents the reading of the thermometer.

Confidence level : $=95\%$

We know that the z-value for 95% confidence interval is 1.96.

Then, we have

$-1.96$      $z=\dfrac{X-\mu}{\sigma}$

$\Rightarrow\ -1.96\sigma$  

But all readings are within 0.6° of $\mu$.

So, $1.96\sigma=0.6$  

$\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061$

Hence, the required standard deviation will be