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 0.1° of μ? (Round your answer to four decimal places.)

Answer 1

The standard deviation would have to be 0.05.

Explanation:

We can solve this problem using the 68-95-99.7 rule for normal distributions:

The rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

What would the value of σ have to be to ensure that 95% of all readings are within 0.1° of μ?

This means that 2 standard deviations would need to be within 0.1 of the mean. So

`2\sigma = 0.1`

`\sigma = (0.1)/(2)`

`\sigma = 0.05`

The standard deviation would have to be 0.05.