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.

Solutions

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 1 year ago

Next > < Previous

Related Solutions

The life in hours of a thermocouple used in a furnace is known to be approximately...

The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with σ=20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. Is there evidence to support the claim that mean life exceeds 540 hours? Use a fixed-level test with =0.05. What is the P-value for this test? What is the -value for this test...

The life in hours of a thermocouple used in a furnace is known to be ap-...

The life in hours of a thermocouple used in a furnace is known to be ap- proximately normally distributed, with standard deviation σ = 20 hours. A random sample of 15 thermocouples resulted in he following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529. Use the 5 steps in the testing procedure to solve following question: a) Is there evidence to support the claim that mean life exceeds 540 hours? Use a...

Question 3 A sheathed thermocouple is placed in a combustion chamber to measure the temperature of...

Question 3 A sheathed thermocouple is placed in a combustion chamber to measure the temperature of the gases at a certain point in the process. The thermocouple reading is 1110K and the inside wall temperature was measured at 1008K. The thermocouple has a surface area of 10 mm2 . (a) A pitot probe is used to measure the velocity of the gas stream in the vicinity of the thermocouple tip. It measures a difference in static and dynamic pressure of...

I wish to use a B-type thermocouple to measure a temperature of 16000C. I am using...

I wish to use a B-type thermocouple to measure a temperature of 16000C. I am using 1000C (boiling water) as my reference temperature. What is the emf expected at 16000C ? (Refer to the NIST thermocouple database): a) 11.233 mv b. 0.033 mV c. 11.263 mV d. None of the above

A thermocouple is being calibrated with a well designed ice bath. The measurements are given in...

A thermocouple is being calibrated with a well designed ice bath. The measurements are given in the table to the right. Using any mathematical tool of your choice,the mean is .174 and standard deviation of the sample is .24228. I recommend excel for this problem and a simple example is included on the module for this class. a) What is the bias error in this sample, assuming a perfect ice bath? b) Assume you have corrected for the bias error...

Q1. You want to keep the indoor temperature of an office at 25oC. The outdoor temperature...

Q1. You want to keep the indoor temperature of an office at 25oC. The outdoor temperature is 5oC. The heat transfer through the building’s exterior is 3 x 106 kJ. To achieve the desired indoor temperature, you are exploring three heat pumps operating between the office interior and: (i) the ground at 12oC; (ii) a pond at 10oC; and (iii) the air outside at 5oC. For each case, what is the minimum theoretical net work input (in kJ) any heat...

4. Suppose that we have a set of temperature measurements in degree Celsius whose variance is...

4. Suppose that we have a set of temperature measurements in degree Celsius whose variance is 25(◦C)2. What is the standard deviation of same set of measurements in degree Fahrenheit? (The formula connecting degree Celsius and degree Fahrenheit is: Y (◦F) = 1.8X(◦C) + 32.) please explain clearly

A thermocouple junction of 1.0-mm in diameter is inserted in a large chamber to measure the...

A thermocouple junction of 1.0-mm in diameter is inserted in a large chamber to measure the temperature of hot gas flowing through the chamber. The hot gas has a velocity of 2 m/s and temperature (Tg) at 800 K. The chamber surface (Ts) is maintained at 500 K. (a) If the thermocouple is at room temperature, Ti when it is inserted in the chamber, calculate the time required for the temperature difference, (Tg–T) to reach 2% of the initial temperature...

1. A black thermocouple measures the temperature in a chamber with black walls. If the air...

1. A black thermocouple measures the temperature in a chamber with black walls. If the air around the thermocouple is at 20°C, the walls are at 100°C, and the heat transfer coefficient between the thermocouple and the air is 15 W /m2·°C, what temperature will the thermocouple read

A spherical thermocouple junction 1.0 mm in diameter is inserted in a combustion chamber to measure...

A spherical thermocouple junction 1.0 mm in diameter is inserted in a combustion chamber to measure the temperature ?T? of the products of combustion. The hot gases have a velocity of V= 5 m/s. (a) If the thermocouple is at room temperature, Ti,when it is inserted in the chamber, estimate the time required for the temperature difference, ?T?-T, to reach 2% of the initial temperature difference, ?T?-Ti. Neglect radiation and conduction through the leads. Properties of the thermocouple junction are...

Subjects