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Usted is a series of experiments and assodioted random variables. In each case, identify the values that the random variable can assume and state whiether the fandom van abe is discrete of continubus. (a) Take a 20-question examination. random vaciable x = number of questions answered correcty Identify the values that the random variable can arsume.
0,1,2=
0,1,2,−20
x>0
0≤x≤20
none of these:
​State whether the random variable is discrete or conkinwous. continuous discrete (b) Observe cars aming at a tolibooth for 5 hours. ransom variable x = number of cars artiving at tollbooth Identity the volues that the mandom variable can assume.
0,1,2,
0,1,2,⋯,24
x>0
0≤x≤5
none of these
​
Sate whether the randem variable is aiscete or cantinveus. continuous discrete (9) Mudit se taxieturifi. State whether the random variable is discrete or continuous. continuous discrete (c) Audit 58 tax returns. random variable x= number of returns containing errors Identify the values that the random variable can assume.
0,1,2,…
0,1,2,…,58
x>0
0≤x≤58
none of these
​State whether the random variable is discrete or continuous. continuous discrete (d) Observe an employee's work. random variable x = number of nonproductive hours in a seven-hour workday Identify the values that the random variable can assume.
0,1,2,…
0,1,2,…,7
x>0
0≤x≤7
​none of these
State whether the random variable is discrete or continuous. continuous discrete d) Observe an employee's work. random variable x= number of nonproductive hours in a seven-hour workday Identify the values that the random variable can assume.
0,1,2,…
0,1,2,…,7
x>0
0≤x≤7
​none of these
State whether the random variable is discrete or continuous. continuous discrete (e) Weigh a shipment of goods. random variable x= number of pounds Identify the values that the random variable can assume.
0,1,2,…
0,1,2,…,16
x>0
0≤x≤1
​none of these
State whether the random variable is discrete or continuous. continuous discrete

Answer 1

A discrete random variable can only take on a countable number of values, while a continuous random variable can take on any value within a given range. In the given scenarios, the identified random variables are all discrete.

Step-by-step explanation:

A discrete random variable can only take on a countable number of values, while a continuous random variable can take on any value within a given range. Let's analyze each scenario:

(a) The random variable x represents the number of questions answered correctly on a 20-question examination. The values that x can assume are 0, 1, 2, ..., 20, so the random variable is discrete.

(b) The random variable x represents the number of cars arriving at a toll booth in 5 hours. The values that x can assume are 0, 1, 2, ..., 24, so the random variable is discrete.

(c) The random variable x represents the number of returns containing errors in 58 tax returns. The values that x can assume are 0, 1, 2, ..., 58, so the random variable is discrete.

(d) The random variable x represents the number of nonproductive hours in a seven-hour workday. The values that x can assume are 0, 1, 2, ..., 7, so the random variable is discrete.

(e) The random variable x represents the number of pounds in a shipment of goods. The values that x can assume are 0, 1, 2, ..., 16, so the random variable is discrete.