Deck 1: Mathematics and Statistics

Question 1

The gamma camera seems to be producing erratic results. A ⁵⁷Co flood source is counted 10 times, producing the following count values: 1000, 975, 1032, 1096, 982, 997, 1012, 1090, 994, 977. What is the chi-square value for these counts?

A) 19.3
B) 18.3
C) 17.3
D) 16.3

Answer 1

17.3

Question 2

How many counts should be acquired into each pixel of a nuclear medicine flood image if it is desired to be 95% confident that the true count in each pixel is within 1% of the measured counts in each pixel?

A) 100,000 counts
B) 40,000 counts
C) 10,000 counts
D) 4000 counts

Answer 2

40,000 counts

Question 3

A patient was injected with ¹³¹I on Monday at 10:00 AM. On Tuesday at 10:00 AM, the thyroid probe was placed over the thyroid and produced 100,000 counts. On Thursday at 10:00 AM, the probe showed 25,000 counts. What is the effective half-life in this patient's thyroid?

A) 12 hours
B) 24 hours
C) 48 hours
D) 72 hours

Answer 3

24 hours

Question 4

A ⁹⁹Mo-^99mTc generator is eluted Monday at 7:00 AM, producing 1.8 Ci of ^99mTc in the eluate vial, in 20 ml saline. What volume of eluate should be withdrawn from the eluate vial into a syringe in order to inject a patient with 20 mCi of ^99mTc at 3:00 PM? (Given the half-life of ^99mTc is 6.02 hours.)

A) 0.56 ml
B) 0.66 ml
C) 0.76 ml
D) 0.86 ml

Question 5

Which expression describes the operation of the gamma camera in question 16?

A) Operating properly
B) Showing too much variation
C) Showing too little variation
D) Not enough information to answer the question

Question 6

A new gamma camera/computer system that uses a new method of calculating cardiac ejection fraction (EF) is installed in a nuclear medicine department. The department decides to calculate EF for the next 25 patients on both the old gamma camera and the new gamma camera before discontinuing the use of the old camera. In the future, if it is desirable to convert the new EF value to that which would have been obtained on the old gamma camera (e.g., to assess if the patient's EF had changed), the mathematical analysis to be used is called a(n)

A) independent t-test.
B) linear regression.
C) standard error.
D) chi-square.

Question 7

If the HVL for some radionuclide in lead is 0.30 mm, what thickness of lead shielding is necessary to reduce the radiation exposure from 8 mR/hr to 1 mR/hr?

A) 0.30 mm
B) 0.45 mm
C) 0.60 mm
D) 0.90 mm

Question 8

The linear attenuation coefficient in lead for ^99mTc gamma rays (140 keV) is 23 cm^-1. What percentage of these gamma rays will be absorbed by a lead apron that contains 0.60 mm of lead?

A) 75%
B) 50%
C) 25%
D) 12.5%

Question 9

A ⁹⁹Mo-^99mTc generator is calibrated for 1.00 Ci of ⁹⁹Mo at 7:00 AM Monday. The generator is eluted daily Monday through Friday at 8:00 AM, but the workload is especially heavy on Friday so the generator is eluted again at 3:00 PM to obtain more ^99mTc. Assuming 100% elution efficiency, how many mCi of ^99mTc will be eluted at 3:00 PM Friday?

A) 930 mCi
B) 710 mCi
C) 160 mCi
D) 80 mCi

Question 10

The radiation intensity from a point source of ^99mTc is 9 mR/hr at 3 m from the source. If the distance is changed to 9 m, what is the new radiation intensity?

A) 0.5 mR/hr
B) 1.0 mR/hr
C) 2.0 mR/hr
D) 3.0 mR/hr

Question 11

20 mCi is equal to how many becquerels?

A)0.74 GBq
B)0.37 GBq
C)0.54 GBq
D)0.20 GBq

Question 12

The dose equivalent for occupational whole-body exposure is commonly limited to 50 mSv. How many rem is this?

A) 5000 rem
B) 500 rem
C) 50 rem
D) 5 rem

Question 13

A patient's thyroid is counted with the thyroid probe and produces 8000 counts. Then the patient is removed and background is found to be 2000 counts. The (net counts) ± (standard deviation in the net counts) in this patient is

A) 10,000 ± 100 counts.
B) 10,000 ± 77 counts.
C) 6000 ± 77 counts.
D) 6000 ± 100 counts.

Question 14

What is the coefficient of variation of 40,000 counts?

A) 2%
B) 1%
C) 0.5%
D) 0.25%

Question 15

A source of is delivered to the nuclear medicine department calibrated for 100 mCi at 8:00 AM on Monday. If this radioactivity is injected into a patient at noon on Tuesday, what radioactivity will the patient receive?

A) 80 mCi
B) 85 mCi
C) 90 mCi
D) 95 mCi

Question 16

A nuclear medicine test produces a positive test result in only 80 of the 100 patients known to be ill. Similarly, the test produces a negative test result in only 190 of the 200 patients known to be not ill. Which is correct?

A) Sensitivity = 80%, specificity = 95%, accuracy = 90%, prevalence = 33%
B) Sensitivity = 90%, specificity = 95%, accuracy = 90%, prevalence = 33%
C) Sensitivity = 90%, specificity = 80%, accuracy = 90%, prevalence = 33%
D) Sensitivity = 90%, specificity = 80%, accuracy = 70%, prevalence = 33%

Question 17

One group of 20 patients is given a drug that is thought to have an effect on kidney function, and another group of 20 patients is given a placebo (i.e., sugar pill, which is known not to have an effect on kidney function). The nuclear medicine gamma camera is used to calculate the glomerular filtration rate (GFR) in these two groups of patients. What would be the proper statistical test to use to test the hypothesis that no difference in GFR exists between these two groups of patients?

A) Chi-square test
B) Paired t-test
C) Independent t-test
D) Linear regression analysis

Question 18

One radiologist is known to be a lax reader compared with another radiologist who is known to be a strict reader. In comparing these radiologists, how would one expect their sensitivity and specificity to compare?

A) The lax reader would have lower sensitivity and higher specificity.
B) The lax reader would have higher sensitivity and lower specificity.
C) The readers would be expected to have the same sensitivity and specificity.
D) Not enough information is given to answer the question.

Question 19

What is the standard deviation of 40,000 counts?

A) 4000 counts
B) 2000 counts
C) 400 counts
D) 200 counts

Question 20

A radioactive source of ¹³⁷Cs (t_1/2= 30 y) was calibrated on October 23, 2000, to contain 10 $\mu$ Ci. This is used as a daily accuracy check source in the dose calibrator. Presuming the dose calibrator is working properly, what activity should the dose calibrator show on April 23, 2006?

A) 9.6 $\mu$ Ci
B) 8.8 $\mu$ Ci
C) 5.4 $\mu$ Ci
D) 2.2 $\mu$ Ci

Question 21

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

A) 36,000 ± 220 cpm
B) 36,000 ± 110 cpm
C) 12,000 ± 55 cpm
D) 12,000 ± 28 cpm

Question 22

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?

A) 24 mCi
B) 18 mCi
C) 12 mCi
D) 6 mCi

Question 23

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?

A) 4.02
B) 3.26
C) 2.15
D) 1.92

Question 24

Convert 5 mBq to kBq and GBq.

A) 50 kBq and 0.5 GBq
B) 500 kBq and 0.05 GBq
C) 5000 kBq and 0.005 GBq
D) 5 *10⁴ and 5 *10 ^{- 4} GBq

Question 25

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

A) 0.49513
B) 0.4951
C) 0.495
D) 0.50

Question 26

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) Yes
B) No
C) There is not enough information to answer the question.
D) None

Question 27

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) 7.5 mCi
B) 5 mCi
C) 2.5 mCi
D) 1.25 mCi

Question 28

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

A) 3.8264
B) 3.826
C) 3.83
D) 3.8

Question 29

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?

A) 92
B) 82
C) 72
D) 62

Question 30

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?

A) 7%
B) 14%
C) 25%
D) 33%

Question 31

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) 9.01
B) 6.28
C) 5.97
D) 4.83

Question 32

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

A) 37 kBq
B) 370 kBq
C) 3.7 MBq
D) 37 MBq

Question 33

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

A) 8 hours
B) 7 hours
C) 6 hours
D) 5 hours

Question 34

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) 26 days
B) 6.3 days
C) 5.1 days
D) 1.2 days

Question 35

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?

A) 10.8 liter
B) 2.74 liter
C) 1.73 liter
D) 0.91 liter

Question 36

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?

A) 0.99
B) 0.95
C) 0.86
D) 0.75

Question 37

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

A) P = 0.001
B) 0.01 < P < 0.05
C) 0.05 < P < 0.1
D) P > 0.10

Question 38

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?

A) 34%
B) 31%
C) 28%
D) 12%

Question 39

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:

A) 9950 to 10,050
B) 9900 to 10,100
C) 9800 to 10,200
D) 9700 to 10,300

Question 40

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) Intercept = 7.15, slope = 0.502
B) Intercept = 6.15, slope = 0.602
C) Intercept = 5.15, slope = 0.702
D) Intercept = 4.15, slope = 0.802

Question 41

An intensity setting of 250 on a display screen may produce a suitable image for a bar phantom with 500K counts in the acquisition. Now it is desired to change to 350K counts in the image. The intensity on the screen is known to change linearly with the intensity control setting. What intensity setting should be used for the new 350K-count image?

A) 100,000
B) 150,000
C) 175,000
D) 200,000

Question 42

The morning elution of the ⁹⁹Mo-^99mTc generator yields 850 mCi of ^99mTc radioactivity in 20 ml of saline eluate. What volume should be withdrawn from the eluate vial into a patient syringe to immediately perform a 25-mCi patient scan?

A) 0.2 ml
B) 0.30 ml
C) 0.59 ml
D) 1.7 ml