Unit 5: Random Variables Name: Date; Class Period; 5.1 Two Types of Random Variables Extra Practice Worksheet Use proper notation and show work. Probability answers should be rounded to 3 decimal places. 1) Discrete or continuous? Classify each of the following random variables as discrete (D) or continuous (C). (a) X = the pH of a water sample that has been randomly selected from a stream (b) Y = the number of correct answers on a recent multiple choice quiz (c) H = the number of homework problems assigned by your statistics teacher yesterday (d) T = the temperature of the turkey meat in a randomly chosen location in a cooked turkey (e) R = the number of times you have to roll a fair, six-sided die to get a 1 2) Working out. A large sample of people aged 19 to 25 were asked, "In the past seven days, how many times did you go to an exercise or fitness center to work out? The random variable X is the number of days they went to an exercise or fitness center. Below is the probability distribution for X. X = Number of Days 0 1 2 3 4 6 7 P(X) 0.68 0.05 0.07 0.08 0.05 0.04 0.01 0.02 (a) Is this a valid probability distribution? Explain. (b) What is the probability a randomly selected person aged 19 to 25 answered with 3 or 4 days? (c) What is the probability a randomly selected person aged 19 to 25 answered with less than 5 days? (d) What is the probability a randomly selected person aged 19 to 25 answer with 0, 1, or 7 days? 3) Spell check? Spell-checking software catches "non-word errors," which result in a string of letters that is not a word (i.e., when "the" is typed as "the" ). When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of non-word errors in a randomly selected essay has the following distribution. (a) Find the missing value of P(X = 2). X = # of Errors 0 1 2 3 4 P(X) 0.1 0.2 7 0.3 0.1 (b) What is the probability of at least 1 error? (c) What is the probability of more than 1 error?Unit 5: Random Variables 4) Discrete or continuous? Classify each of the following random variables as discrete (D) or continuous (C). (a) X = age (in years) of the oldest person in each high school classroom (b) Y = head circumference of a randomly selected female student at a high school (c) H = the number of horses on a farm (d) S = the reported SAT Math score of a randomly selected student from your school (e) T = the winning time in the men's 100-meter dash at your high school's track meet 5) How many languages? The following probability distribution represents X = the number of languages spoken by high school students in the U.S. Languages 3 4 Probability 0.630 0.295 0.065 0.008 0.002 (a) Is X a discrete or continuous variable? Explain. (c) Find the probability a randomly selected U.S. high school student speaks at least 3 language. (d) Find the probability a randomly selected U.S. high school students speak no more than 4 languages. 6) Mice at night. The following probability distribution is for the random variable X = the number of mice caught in traps during a single night in a small apartment building. (a) Is X a discrete or continuous variable? Explain. Mice 0 2 3 4 5 Probability |0.12 0.20 0.31 0.14 0.16 0.07 (b) is the probability distribution valid or not valid? Explain. (c) Find the probability of trapping at least 1 mouse. (d) What is the probability of trapping no less than 3 mice