11:25 Done 1 of 4 MATH 1530 Worksheet 5: Discrete Proba y Distributions Name: Hannah Taylor For all questions, Include proper notation, and round any decimal numbers to four decimal places if necessary. The probability distribution below is based on the numbers of siblings for students in a Statistics class taught by Prof. Brewer (henceforth known as "Stats students"). Use it to answer questions 1-7. Stats Students' Number of Siblings P(X) 0.094 0.421 0.252 0.115 0.066 0.042 0.010 1. What is the probability that a randomly selected Stats student has one sibling? PCX= 17= 0.421 2. What is the probability that a randomly selected Stats student has two or three siblings? 3. What is the probability that a randomly selected Stats student has more than two siblings? P( X 72 ) = 0.233 4. What is the probability that a randomly selected Stats student has at most four siblings? P ( X 4 4) = 0.118 What is the probability that a randomly selected Stats student has at least one sibling? P(X 21 ) = 0.515 Find the population mean of the siblings. Use the appropriate symbol. Find the population standard deviation and variance of the siblings. Use the appropriate symbols +For questions 12-15, a the ding point up. It is dropped six times. 12. What is the probability of the thumbtack landing point up twice? P ( x = 2) binom pdf ( 6, 0. 7, 2) = 0.0595 13. What is the probability of the thumbtack landing point up three or more times? PCx 14. What is the probability of the thumbtack landing point up less than four times? P ( x 74) 1 - binomedf ( 6, 0.7, 4) = 0. 4202 15. What is the expected number of times the thumbtack will land point up out of six? PCx For questions 16-20, in a certain community, 38% of people used the emergency room at the local hospital last year. Assume that 12 people in the community are randomly sampled. 16. What is the probability that five people used the emergency room last year? P ( X = 5) binom pdf ( 12, . 38, 5 ) = 0.2200 17. What is the probability that more than six people used the emergency room last year? P ( x 4) Show exactly what you are plugging into the calculator, for example, inompoff16, 0.7, $1. Round off values to 3 decimal places and label where 1. A thumbtack has a probability of 0.7 of landing point up. It is dropped sixteen times, Find the probability of having it land point up exactly nine times. P(x = 9) bin ompdf (16, 0.7, 9 ) = 0.101 2. If 20% of all automobiles in a large city are foreign-made, find the probability that if there are B automobiles in a parking lot, exactly three are foreign-made. P( X = 3) = binompof ( 8, 0. 20, 3 ) = 0.147 3. Ten percent of the screws produced by an automatic machine are defective. Find the probability that out of 17 screws selected at random, there are exactly three defective screws. P( x = 3) = binompof ( 17, 0.10, 3) = 0.156 4. If each seed in a certain package has a probability of 0.7 of sprouting, and twenty-one seeds are planted, what is the probability that fewer than seventeen seeds will sprout? PCX 5. Suppose that 30 percent of all patients who have received a given medication will have a certain side effect. Find the probability that of fifteen patients who have received the medication more than seven will have the side effect. P( X 2 7 ) = binomedf ( 15, 0. 30, 7) = 0.940 6. A student takes an eight-question true-false exam and guesses on each question. Find the probability of passing if the lowest passing grade is at least six out of eight correct. If the quiz in the previous question was a multiple-choice quiz with five choices for each question, find the probability of passing if the lowest passing grade is at least six out of eight correct.8. All probability distributions have three characteristics. List them below. Shape, Central Tendency, + Variability 9. According to the probability histogram below, what is mean number of defective widgets in one month? Use the appropriate symbol. Defective Widgets in One Month 0 5000 0.4500 1.4000 0.3000 0.2300 0.1500 0.1000 1 1000 0.0500 0.0900 2 Number of Defective Widgets For questions 10-11, a student took a ten-question true or false quiz and guessed randomly on each question. 10. Find the probability that the student will pass the quiz if passing correctly answering at least six out of ten correct. 11. Find the expected number of correct answers if a student makes random guesses for all the questions