MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Module 5 Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Calculate the specified probability ) Suppose that T is a random variable. Given that P(-3. T 3.) = 0.25, and that P(K < -3.) = P(K > 3.), find P(K < -3.). A) 0.25 B).55 C) D) 0.75 Determine the possible values of the random variable. 2) The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let X denote the number of siblings of the student. What are the possible values of the random variable X? Number of siblings Frequency A) 0,, 2, 3,, 5, 6, 7 B) 7 C) 89, 25, 02, 2, 2, 3, 5, 2 D) Brother, sister Find the specified probability. 3) A statistics professor has office hours from 9:00 am to 0:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. x P(X = x) The professor gives each student 0 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait at least 0 minutes to see the professor. A) 0.95 B) 0.0 C) 0.20 D) 0.0 Use random-variable notation to represent the event. ) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of the two numbers. Use random-variable notation to represent the event that the absolute value of the difference of the two numbers is 2. A) {X = 2} B) {(, 3), (2, ), (3, 5), (, 6), (3, ), (, 2), (5, 3), (6, )} C) X = 2 D) P{X = 2} Provide an appropriate response. 5) True or false? For any discrete random variable, the possible values of the random variable form a finite set of numbers. A) True B) False

2 Obtain the probability distribution of the random variable. 6) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form. A) B) C) D) 0 /6 0 /6 0 /6 / /8 3/6 / 2 7/6 2 3/8 2 /2 2 3/8 3 / 3 /8 3 3/6 3 / /6 /6 /6 /6 Calculate the specified probability 7) Suppose that K is a random variable. Given that P(-2.85 K 2.85) = 0.75, and that P(K < -2.85) = P(K > 2.85), find P(K > 2.85). A) B) 0.25 C).25 D) ) Suppose that W is a random variable. Given that P(W 2) = 0.25, find P(W > 2). A) 2 B) C) 0.25 D) 0 Use random-variable notation to represent the event. 9) Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is less than. A) {X < } B) (, ), (, 2), (2, ) C) {X+Y < } D) {X } Determine the possible values of the random variable. 0) Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value of G - R where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y? A) -5, -, -3, -2, -, 0,, 2, 3,, 5 B) 0,, 2, 3,, 5, 6 C) 0,, 2, 3,, 5 D) -6, -5, -, -3, -2, -, 0,, 2, 3,, 5, 6 ) For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. What are the possible values of the random variable Y? A) 0,, 2 B) C) 0,, 2, 3, D), 2, 3, 2) The random variable X is the number of golf balls ordered by customers at a pro shop. Its probability distribution is given in the table. x P(X = x) A) 8.3 B) 9.8 C) 6.5 D) 9 2

3 Find the expected value of the random variable. 3) Sue Anne owns a medium-sized business. Use the probability distribution below, where X describes the number of employees who call in sick on a given day. Number of Employees Sick P(X = x) What is the expected value of the number of employees calling in sick on any given day? A) 2.00 B).75 C).85 D).00 ) The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table A) 2.0 B) 2.00 C) 2.30 D) 2.3 5) The random variable X is the number that shows up when a loaded die is rolled. Its probability distribution is given in the table A) 3.9 B).07 C) 3.50 D) 0.7 The probability distribution of a random variable is given along with its mean and standard deviation. Draw a probability histogram for the random variable; locate the mean and show one, two, and three standard deviation intervals. 6) The random variable X is the number of tails when four coins are flipped. Its probability distribution is as follows. P(X = x) 6 x µ = 2, σ = 3

4 A) B) C) Find the expected value of the random variable. 7) Suppose you buy ticket for $ out of a lottery of,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) -$0.0 B) -$.00 C) -$0.50 D) $0.00

5 8) The probability distribution below describes the number of thunderstorms that a certain town may experience during the month of August. Let X represent the number of thunderstorms in August. Number of storms P(X = x) What is the expected value of thunderstorms for the town each August? A) 2.0 B).6 C).5 D).8 9) A contractor is considering a sale that promises a profit of $3,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $6,000 with a probability of 0.3. What is the expected profit? A) $9,000 B) $8,000 C) $23,800 D) $35,000 20) The random variable X is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is given in the table A) 3.60 B) 3.0 C) 3.35 D)