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

Answer 1

Solution :

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 .

The value of the that 95% of all readings are within 0.5° of is

0.95 = P(|x - | 0.5)

0.95 = 2 (0.5 / ) - 1

0.975 = (0.5 / )

1.96 = 0.5 /

= 0.5 / 1.96 = 0.2551