Question 1

What is the proper number of significant figures for the quotient (6.1 *10^-2)/(0.1232)?

Accepted Answer

The exponent on the 10 specifies how many places the decimal point in the number is to be shifted to the left (for negative exponents) or shifted to the right (for positive exponents).In addition, the accuracy of the result in multiplication or division is such that the product or quotient has the number of significant figures equal to that of the term with the smaller number of significant figures.

Question 2

Using the regression equation in Problem 31, if your training program exam score was 84, what does the regression equation predict for your board score?

Accepted Answer

The standard deviation can be expressed as a percentage of the mean value, which is frequently called the percent standard deviation, or coefficient of variation (CV): 11ea6816_3f2b_b696_b611_8b0d34b64588_TB6242_00 In this problem, the score would be substituted for the mean in the equation.

Question 3

What is the proper number of decimal places in the sum of (0.3) + (3.5264)?

Accepted Answer

For addition and subtraction the final result has the same number of significant decimal places (rather than significant figures) as the number in the problem with the least number of significant decimal places.

Question 4

It is known that 75% of a radionuclide decays away in 12 hours.If starting with 10 mCi, how much will be left after 6 hours?

Accepted Answer

Calculations in nuclear medicine often involve expressing a mathematical concept as a ratio.The equation generally contains several numbers and one unknown value; here the unknown value is (x).The object is to solve for the unknown value by rearranging the terms in the equation.In this situation, the half-life of the material is t hours.Start with 10 mCi.After t hours, there is 5 mCi left.After another t hours, there is 2.5 mCi left.Starting with 10 mCi, after 2t hours, there is 2.5 mCi left, which is only 25% of the initial quantity, and so 75% decayed away.It is given that 75% decays away in 12 hours.So 2t = 12 hours and t = 6 hours.With a half-life of 6 hours, starting with 10 mCi, there would be 5 mCi left after 6 hours.

Question 5

Readers are encouraged to use Microsoft Excel to solve this problem.In a nuclear medicine technology training program, the students wonder if their final exam grade in their training program is related to their subsequent board score on the NMTCB exam.The five students attain the following pairs of scores (exam score, board score) = (72, 60), (84, 74), (88, 71), (68, 60), (91, 79).What is the linear correlation coefficient, r, between exam score and board score?

Accepted Answer

The value of goodness-of-fit parameters helps determine whether it is reasonable that the data points are truly represented by a straight line.The linear correlation coefficient, r, is calculated from the sums used to find the intercept and slope, along with one additional sum from the data points (F1F1F1S1F1F1F10y²): 11ea6816_3f29_93b4_b611_9be767e9aef8_TB6242_00 The sign of the correlation coefficient is merely the same as the sign of the slope.

Question 6

A 5-ml sample of a standard diluted 1:10,000 produces 27,200 counts in the well counter.A 5-ml sample of patient plasma, counted for the same time as the diluted standard sample, produces 99,100 counts.What is the plasma volume?

Accepted Answer

The dilution principle can also be used to measure an unknown volume.Using the dilution principle, it is possible to estimate a patient's plasma volume, C₁V₁ = C₂V₂.Because the standard may be too concentrated, a portion of the standard is diluted and counted while the full-strength undiluted standard can be injected into the patient.The standard can be diluted by adding 1 ml of it to a flask, which is then filled to 500 ml with distilled water.It could then be expressed as a 1:500 diluted standard.The standard counts have to be multiplied by the dilution factor of 500 to obtain the true standard concentration that was injected into the patient.Taking this into consideration, the new equation to be used to calculate the plasma volume would be C₁V₁ = (DF)C₂V_2.

Question 7

Convert 5 mBq to kBq and GBq.

Accepted Answer

The decimal point can be shifted left if the exponent is increased by 1 for each left shift and the decimal can be shifted to the right if the exponent is decreased.

Question 8

The biological half-life of ¹³¹I in a particular patient is 30 days.The physical half-life is 193 hours.If the patient's thyroid is counted with the thyroid probe detector, what effective half-life will be observed?

Accepted Answer

Typically the patient's organ excretes the radiopharmaceutical with some biological half-life t_B while the radioactivity also decays physically with a physical half-life that is denoted as t_P.The counts observed by the gamma camera follow an exponential decay law based on the effective half-life t_E, where: 11ea6816_3f26_fb97_b611_2fd31edcbc3a_TB6242_00 or in a format that is much easier for calculation purposes, 11ea6816_3f26_fb98_b611_a9c678028124_TB6242_11 The effective half-life is always less than or equal to the smaller of t_P or t_B.

Question 9

A patient may have had a kidney function test last month that showed a kidney clearance rate of 45 milliliters per minute (ml/min).The patient returns today and has a kidney clearance rate of 60 ml/min.What is the percent increase in kidney function?

Accepted Answer

Percentages are often used to express percentage change between two values: % change = [(new value - old value)/old value] F1F1F1S1F1F1F10 100.

Question 10

Readers are encouraged to use Microsoft Excel to solve this problem.What is the slope and intercept in the regression equation for problem 31? (board score) = intercept + (slope) * (exam score)

Accepted Answer

The intercept and slope are calculated 11ea6816_3f2b_6875_b611_5f73fb1940d2_TB6242_00

Question 11

A thyroid uptake dose of 10 $\mu$Ci is equal to how much radioactivity in SI units?

Accepted Answer

The curie = 3.7 *10¹⁰ disintegrations per second [dps], and the Bq =1 dps; therefore, 1 Ci = 37 GBq and 1 mCi = 37 MBq and 1$\mu$Ci = 37 kBq.

Question 12

Readers are encouraged to use Microsoft Excel to solve this problem.What is the coefficient of variation (CV) of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Accepted Answer

The standard deviation is a percentage of the mean value, which is frequently called the percent standard deviation, or coefficient of variation (CV): 11ea6816_3f29_6ca3_b611_a914546932d5_TB6242_00

Question 13

Using Table 1-9 in the book, does a linear correlation coefficient r = 0.95 for n = 5 data points indicate a statistically significant linear relationship between the x and y variables?

Accepted Answer

A correlation r = 1 is a perfect fit, with the straight line passing exactly through each data point.The closer r is to 1, the more highly correlated are the x and y data.A chance, or probability (P), always exists that data that are truly not linearly related to each other will randomly appear in a fairly linear fashion.The statistical significance of correlation values less than 1 must be evaluated from statistical tables of probability.

Question 14

A source of ¹⁸F (t_1/2 = approximately 2 hr) is noted to contain 3 mCi at noon.What was the radioactivity at 8:00 AM that same day?

Accepted Answer

The radioactive decay law can be algebraically rearranged (dividing both sides of the decay equation by A₀) as: A/A₀ = e^-^0.693F1F1F1S1^F1F1F10F1F1F1S1^F1F1F10⁽^t/t_1/2⁾.

Question 15

Readers are encouraged to use Microsoft Excel to solve this problem.What is the standard deviation of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Accepted Answer

The standard deviation, a measure of the precision of the data, is given by the symbol F1F1F1S1F1F1F10, defined as: 11ea6816_3f28_f770_b611_9bf500e3ef7e_TB6242_00 Recall that an exponent of 11ea6816_3f28_f771_b611_f52213609d7b_TB6242_11 means the same as the square root 11ea6816_3f29_4592_b611_07d9864d7c9d_TB6242_11 .The standard deviation is a measure of the deviation or spread of the data points from the mean value.The standard deviation is often expressed in a format of the mean value ±F1F1F1S1F1F1F10.A large F1F1F1S1F1F1F10 value indicates data with a large range and, therefore, poor precision.

Question 16

Using Table 1-9 in the book, what is the P value for the linear correlation coefficient r in question 31?

Accepted Answer

A correlation r = 1 is a perfect fit, with the straight line passing exactly through each data point.The closer r is to 1, the more highly correlated are the x and y data.A chance, or probability (P), always exists that data that are truly not linearly related to each other will randomly appear in a fairly linear fashion.The statistical significance of correlation values less than 1 must be evaluated from statistical tables of probability.

Question 17

A radioactive source decays from 20 mCi to 2.5 mCi in 18 hours.What is the physical half-life?

Accepted Answer

The 11ea6816_3f27_49b9_b611_b39ab469e7ea_TB6242_11 , which depends on the radioactive material involved, is the time in which the activity is decreased to half its original value.The radioactive decay law may alternatively be expressed as 11ea6816_3f27_49ba_b611_67934f7dd263_TB6242_11 The factor 0.693 is actually ln 2, which is commonly written with three significant figures.Each half-life of radioactive decay causes the activity level to drop by 50%.

Question 18

A long-lived radioactive source is counted for 1 minute and yields 10,000 counts.If this source is counted immediately again, there is a 95% probability that the result will be in the range:

Accepted Answer

Counting statistics, besides being Poisson, are also described by a Gaussian distribution as long as the number of counts is greater than approximately 30.Hence given some number of counts C, the standard deviation is automatically known.It is also known that 68% of repeat measures of the sample fall within C ± 11ea6816_3f27_e5fc_b611_6d29a67e5585_TB6242_11 and 95% of repeat measures of the sample fall within C ± 11ea6816_3f27_e5fd_b611_c95e5f862ad8_TB6242_11 , and so on: 95% confidence = C ± 2F1F1F1S1F1F1F10_c = C ± 11ea6816_3f28_0d0e_b611_7f3c275e31c9_TB6242_11 .

Question 19

Readers are encouraged to use Microsoft Excel to solve this problem.What is the mean of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Accepted Answer

Precision refers to the spread, or range, of data values obtained when some parameter is measured many times or in many patients.A small precision means that little variation exists in the data values.Then, the mean (or average) of the n values of the parameters x is defined by the symbol: 11ea6816_3f28_a94f_b611_375fa293fb7e_TB6242_11 The symbol F1F1F1S1F1F1F10x means the sum of all the measurements of x.

Question 20

A sample shows a count rate of 36,000 cpm during a 3-minute counting period.Express this as the count rate ± standard deviation.

Accepted Answer

Counting statistics, meaning the number of counts expected from a sample, follow the Poisson distribution.In the Poisson distribution, the standard deviation (F1F1F1S1F1F1F10_C) for any number of counts (C) is fixed at the square root of C: 11ea6816_3f27_97db_b611_8508dbadacee_TB6242_11 This fixed definition of standard deviation does not exist in Gaussian distributions; essentially only counting statistics are Poisson.In this problem, cpm must be calculated first.

Quiz 1: Mathematics and Statistics

What is the proper number of significant figures for the quotient (6.1 *10^-2) /(0.1232) ?

Using the regression equation in Problem 31, if your training program exam score was 84, what does the regression equation predict for your board score?

What is the proper number of decimal places in the sum of (0.3) + (3.5264) ?

It is known that 75% of a radionuclide decays away in 12 hours.If starting with 10 mCi, how much will be left after 6 hours?

A 5-ml sample of a standard diluted 1:10,000 produces 27,200 counts in the well counter.A 5-ml sample of patient plasma, counted for the same time as the diluted standard sample, produces 99,100 counts.What is the plasma volume?

Convert 5 mBq to kBq and GBq.

The biological half-life of ¹³¹I in a particular patient is 30 days.The physical half-life is 193 hours.If the patient's thyroid is counted with the thyroid probe detector, what effective half-life will be observed?

A patient may have had a kidney function test last month that showed a kidney clearance rate of 45 milliliters per minute (ml/min) .The patient returns today and has a kidney clearance rate of 60 ml/min.What is the percent increase in kidney function?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the slope and intercept in the regression equation for problem 31? (board score) = intercept + (slope) * (exam score)

A thyroid uptake dose of 10 $\mu$ Ci is equal to how much radioactivity in SI units?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the coefficient of variation (CV) of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Using Table 1-9 in the book, does a linear correlation coefficient r = 0.95 for n = 5 data points indicate a statistically significant linear relationship between the x and y variables?

A source of ¹⁸F (t_1/2 = approximately 2 hr) is noted to contain 3 mCi at noon.What was the radioactivity at 8:00 AM that same day?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the standard deviation of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Using Table 1-9 in the book, what is the P value for the linear correlation coefficient r in question 31?

A radioactive source decays from 20 mCi to 2.5 mCi in 18 hours.What is the physical half-life?

A long-lived radioactive source is counted for 1 minute and yields 10,000 counts.If this source is counted immediately again, there is a 95% probability that the result will be in the range:

Readers are encouraged to use Microsoft Excel to solve this problem.What is the mean of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

A sample shows a count rate of 36,000 cpm during a 3-minute counting period.Express this as the count rate ± standard deviation.

Quiz 1: Mathematics and Statistics

What is the proper number of significant figures for the quotient (6.1 *10-2) /(0.1232) ?

Using the regression equation in Problem 31, if your training program exam score was 84, what does the regression equation predict for your board score?

What is the proper number of decimal places in the sum of (0.3) + (3.5264) ?

It is known that 75% of a radionuclide decays away in 12 hours.If starting with 10 mCi, how much will be left after 6 hours?

A 5-ml sample of a standard diluted 1:10,000 produces 27,200 counts in the well counter.A 5-ml sample of patient plasma, counted for the same time as the diluted standard sample, produces 99,100 counts.What is the plasma volume?

Convert 5 mBq to kBq and GBq.

The biological half-life of 131I in a particular patient is 30 days.The physical half-life is 193 hours.If the patient's thyroid is counted with the thyroid probe detector, what effective half-life will be observed?

A patient may have had a kidney function test last month that showed a kidney clearance rate of 45 milliliters per minute (ml/min) .The patient returns today and has a kidney clearance rate of 60 ml/min.What is the percent increase in kidney function?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the slope and intercept in the regression equation for problem 31? (board score) = intercept + (slope) * (exam score)

A thyroid uptake dose of 10 μ\muμ Ci is equal to how much radioactivity in SI units?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the coefficient of variation (CV) of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Using Table 1-9 in the book, does a linear correlation coefficient r = 0.95 for n = 5 data points indicate a statistically significant linear relationship between the x and y variables?

A source of 18F (t1/2 = approximately 2 hr) is noted to contain 3 mCi at noon.What was the radioactivity at 8:00 AM that same day?

Readers are encouraged to use Microsoft Excel to solve this problem.What is the standard deviation of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

Using Table 1-9 in the book, what is the P value for the linear correlation coefficient r in question 31?

A radioactive source decays from 20 mCi to 2.5 mCi in 18 hours.What is the physical half-life?

A long-lived radioactive source is counted for 1 minute and yields 10,000 counts.If this source is counted immediately again, there is a 95% probability that the result will be in the range:

Readers are encouraged to use Microsoft Excel to solve this problem.What is the mean of the following five numbers: 6.40, 7.20, 3.50, 9.20, 5.10?

A sample shows a count rate of 36,000 cpm during a 3-minute counting period.Express this as the count rate ± standard deviation.

What is the proper number of significant figures for the quotient (6.1 *10^-2) /(0.1232) ?

The biological half-life of ¹³¹I in a particular patient is 30 days.The physical half-life is 193 hours.If the patient's thyroid is counted with the thyroid probe detector, what effective half-life will be observed?

A thyroid uptake dose of 10 $\mu$ Ci is equal to how much radioactivity in SI units?

A source of ¹⁸F (t_1/2 = approximately 2 hr) is noted to contain 3 mCi at noon.What was the radioactivity at 8:00 AM that same day?