Exam 1: Mathematics and Statistics

What is the standard deviation of 40,000 counts?

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 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)

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?

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

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 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?

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?

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 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:

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 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 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 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?

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?

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?

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, 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 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?