Question

In: Statistics and Probability

A thermocouple is used to measure a known temperature of 25oC. A set of measurements is...

A thermocouple is used to measure a known temperature of 25oC. A set of measurements is taken. 29.6% of the measurements are found within ±1 oC of 25oC (the sample mean value is 25oC). We assume the temperature to be a random variable following a Gaussian distribution function. Please answer the below questions and upload your work as a single file (preferably PDF or jpeg). You need to show ALL work.

Question 1. Show that the standard deviation of the thermocouple σ is equal to 2.63oC. Show all steps to obtain the result. Use this value of the standard deviation σ in the subsequent questions.

Question 2. What is the probability that a temperature reading is greater than 27oC? Show all steps to obtain the result.

Question 3. What is the probability that a temperature reading is less than 26.5oC? Show all steps to obtain the result.

Question 4. Determine the 95% confidence interval of the mean temperature μ. Note that the number of pressure readings is 50.

Expert Solution

Question 1

We need to find the Z score for given deviation, and use the Z table to find the probability, which is given to us as 29.6%. Since the Gaussian distribution is symmetric, the probabiity to deviate on one side (i.e. temperature lies from 25 to 26) is 14.8%. Hence,

Looking up the Z table, we get P(Z < z) = 0.648 occurs at z = 0.38. Hence,

Question 2

Again we need to find Z score, based on sigma derived above

Question 3

We need to find standard error

The Z value for two sides 95% confidence interval is ±1.96 Hence, interval is obtained as

orchestra answered 2 years ago

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