Question

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?

a. X = {0, 1, 2, 3}
b. X = {1, 2, 3}
c. X = {0, 1, 2}
d. X = {0, 1}

Answer 1

The random variable X represents the number of days Ellen practices music in a week and it can take on the values 0, 1, 2, and 3, which means the correct answer is option a. X = {0, 1, 2, 3}.

Step-by-step explanation:

The values that the random variable X can take on are based on the frequency of Ellen's music practice days within a week. Based on the information given, X represents the number of days Ellen practices music in a week. Here are the possible values of X:

• 3 days: Ellen practices music three days a week 85% of the time.
• 2 days: She practices for two days 8% of the time.
• 1 day: She practices for one day 4% of the time.
• 0 days: She does not practice any days 3% of the time.

Therefore, the random variable X can take on the values 0, 1, 2, and 3, which corresponds to option a. X = {0, 1, 2, 3}.