Chapter 6 Test Review Name TRUE-FALSE: Determine whether each of the following statements is true or false. 1) A random variable is continuous when the set of possible values includes an entire interval on the number line. 2) For a continuous random variable x, the area under the density curve over an interval a to b represents the probability that x is between a and b. ) For a continuous random variable x, P( x 6) = p() + p(4) + p(5) + p (6). 4) The binomial probability distribution is an example of a continuous probability distribution. MULTIPLE CHOICE: Circle the correct choice for each question. 5) Which of the following is true about every random variable I. It takes on numerical or categorical values. II. It describes the results of a random phenomenon. III. Its behavior can be described by a probability distribution. A) I only B) II only C) III only D) II and III E) I, II, and III 6) Let be the outcome of rolling a fair six-sided die. P( 2 5) < = A) 1/6 B) 1/ C) 1/2 D) 2/ E) 5/6 7) An ecologist studying starfish populations collects the following data on randomly selected 1 meter by 1 meter plots on a rocky coastline. - The number of starfish in the plot - The total weight of starfish in the plot. - The percentage of area in the plot that is covered by barnacles (a popular food for starfish) - Whether or not the plot is underwater midway between high and low tide. 8) How many of these measurements can be treated as continuous random variables and how many as discrete random variables? A) Three continuous, one discrete. B) Two continuous, two discrete. C) One continuous, three discrete. D) Two continuous, one discrete, and a fourth that cannot be treated as a random variable. E) One continuous, two discrete, and a fourth that cannot be treated as a random variable. 9) Sule s job is just a few bus stops away from his house. While it can be faster to take the bus to work, it s more variable, because of variations in traffic. He estimates that the commute time to work by bus is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes. The commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with a standard deviation of 1 minute. What is the probability that the bus will be faster than walking? A) 0.840 B) 0.8485 C) 0.8980 D) 0.9756 E) 0.9896
10) Which of the following variables is a continuous variable? A) the lifetime of a 9-volt battery B) the number of cracked eggs in a carton of 12 eggs C) the number of people in a family D) the brand of laundry detergent used 11) Which is NOT correct: For any continuous variable, A) P ( a) = 1 P( < a) B) P( > a) = 1 P( a) C) P ( a) = P( < a) D) P( a < < b) = P( a b) For #12-14, consider the following: The local library allows the checking out of up to five books at any one time. Based on historical records, x = the number of books checked out by an individual has the following population distribution. x 0 1 2 4 5 p(x).20.2.18.15.10.05 12) What is P(1 < x 4)? A).4 B).42 C).75 D).48 1) What is the mean number of books to be checked out by an individual? A) 15 B) 1.78 C) 7.5 D) 1 14) What is the standard deviation of books to be checked out by an individual? A) 1.49 B) 2.072 C) 2.680 D) 1.67 15) Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewoman is 66 inches with a standard deviation of inches. If a committee looks at all ways of pairing up one male with one female officer, what will be the mean and standard deviation for the difference in heights for the set of possible partners? A) Mean of 5 inches with a standard deviation of 1 inch. B) Mean of 5 inches with a standard deviation of.5 inches. C) Mean of 5 inches with a standard deviation of 5 inches. D) Mean of 68.5 inches with a standard deviation of 1 inch. E) Mean of 68.5 inches with a standard deviation of.5 inches. 16) A widget manufacturer estimates that the total weekly cost in dollars, C, to produce x widgets is given by the linear function C(x) = 500 + 10x, where the intercept 500 represents a fixed cost of manufacture and the slope 10 represents the variable cost of producing a certain number of widgets. Analysis of weekly widget production reveals that the number of widgets produced in a week is a random variable with mean μ = 200 and standard deviation σ = 20. What are the mean and the standard deviation of C? A) mean of C = $2500, standard deviation of C = $200 B) mean of C = $2500, standard deviation of C = $700 C) mean of C = $100,010, standard deviation of C = $10,000 17) A national study found that the average family spent $422 a month on groceries, with a standard deviation of $84. The average amount spent on housing (rent or mortgage) was $1,120 a month, with a standard deviation $212. The expected total amount a family spends on food and housing is $1542. What is the standard deviation of the total? A) $128 B) $148 C) $228 D) $295
18) If x is a binomial random variable with n = 10 and p =.25, then 2 A) σ = 1.875 B) σ = 2.5 C) σ = 1.875 D) σ = 1.875 19) Which of the following is not a property of a geometric experiment? A) It consists of a fixed number of trials n. B) Outcomes of different trials are independent. C) The probability of success is the same for all trials. D) Each trial can result in one of two possible outcomes. 20) The probability that any one driver will blow past the stop sign in front of Karen s house is.84. Of ten drivers randomly selected, what s the probability that less than seven drivers blow past it? A).061 B).048 C).145 D).206 21) If a is a binomial random variable with n = 10 and p =.4, then the binomial probability function can be written as A) =.4.6 px ( ) 10C4( x) (1 x ) B) px ( ) = 10C x(.4) (.6) C) px ( ) = C (.6) (.4) D) px ( ) = C (.4) (.6) 10 x For #22-24, consider the following: A fair die will be rolled until a five appears. Let x = the number of rolls required in order to roll a five. 22) What s Px ( = 6)? A).5 B).402 C).167 D).067 x 10 2) What s Px ( = 0)? A).167 B).8 C) 0 D) 1 24) What s Px ( > )? A).579 B).116 C).694 D).421 25) In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, which of the following represents the probability that you win at least once? A) ( ) 5 0.2 B) 1 ( 0.2) 5 C) 1 ( 0.8) 5 5 0.2 0.8 1 5 0.2 0.8 1 D) ( )( ) 4 E) ( 0.8 ) 5 + ( )( ) 4
26) Roll one 8-sided die 10 times. The probability of getting exactly sevens in those 10 rolls is given by 5 10 1 7 A) 7 10 1 7 B) 5 8 1 7 C) 7 8 1 7 D) 7 10 7 1 E) 27) The binomial expression 8 2 2 6 1 2 C gives the probability of A) at least 2 successes in 8 trials if the probability of success in one trial is 1/. B) at least 2 successes in 8 trials if the probability of success in one trial is 2/. C) exactly 2 successes in 8 trials if the probability of success in one trial is 1/. D) exactly 2 successes in 8 trials if the probability of success in one trial is 2/. E) at least 6 successes in 8 trials if the probability of success in one trial is 2/. 28) Which of the following is a binomial random variable? A) The number of tosses before a 5 appears when tossing a fair die. B) The number of points a hockey team receives in 10 games, where two points are awarded for wins, one point for ties, and no points for losses. C) The number of hearts out of five cards drawn from a deck of 52 cards, without replacement. D) The number of motorists not wearing seat belts in a random sample of five drivers. 29) Suppose we have a random variable where the probability associated with the value for k=0, 8. What is the mean of? A) 0.45 B) 0.55 C) 1.98 D).6 E) 4.4 0) An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items in perfect condition. If in reality 90% of the whole lot are perfect, what is the probability that the lot will be accepted? A) 0.600 B) 0.667 C) 0.729 D) 0.810 E) 0.972 1) A judge is chosen at random reaches a just decision roughly 80% of the time. What is the probability that in three randomly chosen cases at least two out of three judges reach a just conclusion? A) B) C) D) E)
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