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?

0.3061.

Step-by-step explanation:

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

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

Confidence level :

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

Then, we have

But all readings are within 0.6° of .

So,  

Hence, the required standard deviation will be