STA2023 chapter 5 practice

In a probability distribution of a discrete random variable, the probability of each value of the random variable occurring lies between what two numbers? 0 and 1 0 and 2 -1 and 1 -1 and 0

0 and 1

One of the most profitable items at Al's Auto Security Shop is the remote starting system. Let x be the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past 80 days. a. Construct a probability distribution table for the number of remote starting systems installed on a given day. x| 1 2 3 4 5 P(x) a2. Choose the graph of the probability distribution. b.Are the probabilities listed in the table of part a exact or approximate probabilities of the various outcomes? exact probabilities or approximate probabilities c. find the following probabilities. i. P(x=5) ii. P(x> or= 3) iii. P(2 < or = x < or = 4) iv. P(x<5)

a. 0.10 0.25 0.30 0.20 0.15 a2. e b approximate probabilities c. 0.15 0.65 0.75 0.85

The following table gives the probability distribution of a discrete random variable x. find the following probabilities. a. P(x=1) b. P(x< or = 1) c. P(x > or =3) d. P(0< or= x < or= 2)

a. 0.12 b. 0.15 c. 0.61 d. 0.39

a.The number of new accounts opened at a bank during a certain month: continuous or discrete b.The time take to run a marathon: continuous or discrete C. The price of a concert ticket: discrete or continuous d. The number of rotten eggs in a randomly selected box: continuous or discrete e.The points scored in a football game: continuous or discrete f.The weight of a randomly selected package: continuous or discrete

a. discrete b. continuous c. continuous d. discrete e. discrete f. continuous

Each of the following tables lists certain values of x and their probabilities. Determine whether or not each one satisfies the two conditions required for a valid probability distribution. a. x| 5 6 7 8 P(x)| -0.45 0.45 0.63 0.26 the table ( represents or does not represent) a valid probability distribution. b. x| 1 2 3 P(x)| 0.34 0.22 0.44 the table (represents or does not represent) a valid probability distribution) c. x| 0 1 2 3 P(x)| 0.19 0.05 0.40 0.64 the table (represents or does not represent) a valid probability distribution)

a. does not represent b. represents c. does not represent

let x be a binomial random variable that denotes the number of people in a random sample of 20 Americans who do not know that GOP stands for Grand Old Party. What are the possible values that x can assume? - the random variable x can assume any of the values between 0 and 12. - the random variable x can assume any of the integer variables between 0 and 11 - the random variable x can assume any of the integer values between 1 and 20 -the random variable x can assume any of the values between 0 and 20 - the random variable x can assume any of the integer values between 0 and 20. b. Find the probability that exactly 11 people in a random sample of 20 Americans do not know that GOP stands for Grand Old Party. Use the binomial probability distribution formula. round your answer to four decimal places. P=

a. the random variable x can assume any of the integer values between 0 and 20 b. 0.1771

The amount of rainfall in a city during a specific month is -continuous random variable -discrete random variable

continuous random variable

The amount of time taken by a randomly selected student to complete a statistics exam is a -discrete random variable -continuous random variable

continuous random variable

One of the four gas stations located at an intersection of two major roads is a Texaco station. Suppose the next six cars that stop at any of these four gas stations make their selections randomly and independently. Let x be the number of cars in these six that stop at the Texaco station. Is x a discrete or a continuous random variable? -continuous -discrete

discrete

The number of students on a waitlist to register for a class is a discrete random variable. -true -false

true

Is the statement "A random variable that can assume any value contained in one or more intervals is called a continuous random variable." true or false?

ture