(Solved): 1) Hemocytometer slides are used to count cells and other microscopic particles. They consist of gl ...

1) Hemocytometer slides are used to count cells and other microscopic particles. They consist of glass engraved with a laser-etched grid. The size of the grid is known making it possible to count the number of particles in a specific volume of fluid. A hemocytometer slide used to count red blood cells has 160 squares. The average number of blood cells per square is 4.375 . What is the probability that one square contains between 3 and 6 cells? 2) People whose blood type is O-negative are universal donors - anyone can receive a blood transfusion of O-negative blood. In the United States, $7.2\%$ of the people have O-negative blood. A blood donor clinic wants to find 100 -negative individuals. In repeated screening, what is the chance of finding such individuals among the first 100 people screened? Read problem 5.25 and answer the following questions. a. Screening individuals until finding 10 with O-negative blood type and counting the number of individuals screened can be modeled with a Negative Binomial distribution. Explain why the number of screening has a Negative Binomial probability distribution. Explain why $r=10$. $P=0.072$. b. What is the expected number of individuals who must be screened to find 10 with O-negative blood type? Hint: Appendix B. c. What is the standard deviation of the number of individuals who must be screened to find 10 with O-negative blood type? Hint: Appendix B. d. What is the probability that the $10^{\text{th }}$ person with O-negative blood type is found on the $100^{\text{th }}$ person? In R, help(dnbinom) gives information on the probability mass/density function for a Negative Binomial random variable as implemented in $\mathrm{R}$. R chooses to count the number of failures instead of the number of trials/screenings. Use formula dnbinom(\# failures; \# success, probability). In this question, number of trials $=100$, number of success $=10$, and number of failures $=100?10=90$. e. What is the probability that the $10^{\text{th }}$ person with O-negative blood type is found on by $100^{\text{th }}$ person? In R, help(pnbinom) gives information on the cumulative probability function for a Negative Binomial random variable as implemented in $R$. R chooses to count the number of failures instead of the number of trials/screenings. Use formula pnbinom (\# failures, \# success, probability). In this question, number of trials $=100$, number of success $=10$, and number of failures $=100?10=90$.