Practice Questions 3 final

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1 Practice Questions 3 Chapter 5: 1. List the 4 elementary properties of probability presented in the text. 2 pts. 1. Property 1(range of possible probabilities): “ Individual probabilities are never less than 0 and never more than 1” (Gerstman, 2015, p. 170). 2. Property 2(total probability): “ Probabilities in the sample space must sum exactly to 1”(Gerstman, 2015, p. 170) 3. Property 3 (Complements ): “The probability of a complement is equal to 1 minus the probability of an event” (Gerstman, 2015, p. 170). 4. Property 4 (Disjoint events): “Events are disjoint if they cannot exist simultaneously” (Gerstman, 2015, p. 170). 2. What does AUC stand for? 1 pt The area under the curve Chapter 6: 3. If you assume that 20% of the nurses in the hospital smoke and you select 4 nurses at random. In what percentage of samples will all 4 people be smokers? 1 pt N=4; p= .2 Q=1-> 1-0.2= 0.8 Probability of four successes: Pr(x=4): 1x (0.20)^4 x1 = 0.0016 = 0.16% 4. A rapid screening test for HIV has a false positive rate of 0.5%. This means that the probability of a false positive test is 0.005. If the test is used in 500 HIV-free individuals, what is the expected number of false positives in the sample? In addition, what is the probability of encountering no false positives in the sample? 2 pt N= 500 P= 0.005 Q= 1-0.005=0.995 =np μ  2.5 P(x=0)=1x1x0.08157= =0.08157; as a percent = 8.2%

2 Chapter 7: 5. Fill in the blank: 68% of the area under a Normal curve is within the mean +/- 1 standard deviation. 95% is within the mean +/- 2 standard deviations and 99.7% is within the mean +/- 3 standard deviations. 2pts 6. Water samples from a particular site demonstrates a mean coliform level of 10 organisms per liter with standard deviation 2. Values vary according to a Normal distribution. What percentage of samples will contain more than 15 organisms? 3 pts Μean=10 SD=2 X= organisms 15-10/2=2.5 Table B shows that 0.62% of sample will contain organisms greater than 15. 7. The gestation in uncomplicated human pregnancies from birth to conception varies according to a Normal distribution with a mean of 39 weeks and standard deviation of 2 weeks. What is the 99 th percentile of this distribution? In other words what gestational length is greater than or equal to 99% of the other normal gestations? 4 pts Mean= 39 SD=2 0.99 X= 39+2(2.33 )=43.66 8. The SAT and ACT are standardized tests for college admission in the United States. Both tests include components that measure reading comprehension. Suppose that SAT critical reading scores are Normally distributed with a mean of 510 and standard deviation of 115. In contrast, ACT reading scores are Normally distributed with a mean of 20.5 and standard deviation of 5. Sam takes the SAT reading test and scores 660. Dave takes the ACT test and scores 28. Who had the superior score, Sam or Dave? 10 pts SAT(SAM) Mean=510 SD=115

3 ACT(DAVE) Mean= 20.5 SD=5 Z= x-mean/ SD Sam: 660-510/115= 1.30 Dave: 28-20.5/5=1.5 Dave had the superior score because, between the two scores shown above, Dave has a larger z score of 1.5 standard deviations above the mean (Gerstman, 2015). 25 points

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4 References Gerstman, B. (2015). Basic biostatistics: Statistics for public health practice second edition/access code (2nd ed.). Jones and Bartlett Learning.

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