A study sought to understand binge drinking in teenagers. After surveying 100 high school students about the most number of alcoholic drinks ever had at a party, the researcher conveyed what she found with the following random variable: X = “largest number of drinks in a single night” with probability distribtion x P(X=x) 0 20/100 1 23/100 2 17/100 3 16/100 4 12/100 5 7/100 6 3/100 7 2/100 Answer the following. (1) What is the probability that a teen has never had a drink? (2) What is the probability that a teen has had 5 or more drinks? (3) Compute E(X).
A study sought to understand binge drinking in teenagers. After surveying 100 high school students about the most number of alcoholic drinks ever had at a party, the researcher conveyed what she found with the following random variable:
X = “largest number of drinks in a single night”
with probability distribtion
x P(X=x)
0 20/100
1 23/100
2 17/100
3 16/100
4 12/100
5 7/100
6 3/100
7 2/100
Answer the following.
(1) What is the probability that a teen has never had a drink?
(2) What is the probability that a teen has had 5 or more drinks?
(3) Compute E(X).
(4) Interpret what E(X) means in the context of this study.
(5) Compute the standard deviation of X.
2. Consider a statistical experiment where you flip two coins and you are interested in how many heads flipped.
(1) Write a description of the random variable describing this experiment, i.e. X = ”some description”
(2) Write a probability distribution describing the probability of the outcomes of this
(3) What is the expected number of heads flipped?
(4) What is the variance and standard deviation of the number of heads flipped?
3. Consider a study that surveyed 50 people to rate how much they like their job. Ratings mean 1 for “hate my job”, 2 for “dislike my job”, 3 for “neutral”, 4 for “like my job” and 5 for “love my job”. This survey found that
• 8 people hated their job
• 14 people disliked their job
• 15 people were neutral
• 9 people liked their job, and
• 4 people loved their job.
(1) Write a description of the random variable describing this survey
(2) Write a probability distribution describing the probability of the outcomes of this event.
(3) What probability of people like their job?
(4) Calculate the expected rating.
4. Is X a random variable if it has a probability distribution? Why or why not?
x P(X=x)
1 0.45
2 0.31
3 0.29
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