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? (round your answer to four decimal places.) σ =

 0.2551

Step-by-step explanation:

Given : 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.

Significance level :

The critical z-value for 95% confidence : (1)

Since , (where x be any random variable that represents the temperature reading from a thermocouple.)

Then, from (1)

    (2)

Also,  all readings are within 0.5° of μ,

i.e.

i.e.   [From (2)]

i.e.  

i.e.

The required standard deviation :

30

step-by-step explanation:

times by times