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WorksheetsProbability Distribution Functions -Practice quiz
Total questions: 20
Worksheet time: 17mins
(a)
Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most 4 packs. Suppose that each pack has a probability of 0.2 of containing the card Hugo is hoping for.
Let the random variable X be the number of packs of cards Hugo buys. Here is the probability distribution for X:
What is the probability that Hugo buys fewer than 3 packs of cards?
(a)
A data scientist tracked how many cups of coffee she drank every day at work over the course of a year. She used the data to build a probability distribution where the random variable C represents the number of cups of coffee she drank on a given day. Here is the partially completed distribution:
(a)
Cora is playing a game that involves flipping three coins at once.
Let the random variable H be the number of coins that land showing "heads". Here is the probability distribution for H:
(a)
Can the function in the given table be a probability distribution function?
Yes, because all the probabilities are between 0 and 1
No, because the sum of the probabilities is not 1
Yes, because the sum of the probabilities is 1
Yes, because it is in a table format.
No, because some probabilities are less than zero.
The function in the given table is a probability distribution function of a discrete random variable 𝑋. Find the value of 𝑎.
21
107
103
101
52
Write your answer as a fraction in its simplest form. use the / symbol e.g. 1/3
(a)
Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.
Find the probability that exactly 13 patients visit the clinic in a given hour.
(write your answers to 2 decimal places)
(a)
Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.
Find the probability that at least 13 patients visit the clinic in a given hour.
(write your answers to 2 decimal places)
(a)
Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.
Find the probability that at most 13 patients visit the clinic in a given hour.
(write your answers to 2 decimal places)
(a)
Let X be the number of heads obtained when tossing
a fair coin 3 times.
What are the possible values of X?
0,1,2,3,
1,2,3,
0,1,2,3,4
1,2,3,4
Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no events 5% of the time.
Given that X is the random variable for the number of times he does an event in a month, what values does x take on?
0,1,2,3,4,5
1,2,3,4,5
0,1,2,3,4
1,2,3,4
A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
Complete Table 4.19 using the data provided.
P(x = 4) = (a)
A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution.
Let X = the number of years a new hire will stay with the company.
Let P(x) = the probability that a new hire will stay with the company x years.
Complete Table 4.19 using the data provided and calculate
P(x ≥ 5) = (a)
The table below shows the probability distribution for winning a prize in a game of chance.
What is the probability of truly winning money that is more than $0?
(a)
The table below shows the probability distribution for winning a prize in a game of chance.
What is the probability of winning $10 or more?
(a)
The table below shows the probability distribution for winning a prize in a game of chance.
What is the probability of winning less than $10?
(a)
The random variable X has the probability distribution shown.
Use the fact that probabilities add up to 1 to find the value of c.
(write your answer to 2 decimal placed)
(a)
A fair coin is tossed twice. Let X be the number of heads that are observed.
By constructing the probability distribution of X, find the probability that at least one head is observed.
(write your answer to 2 decimal places)
(a)
Fill in the missing word to complete the sentence;
If a coin is tossed 5 times and the random variable X is the
number of heads that are recorded, then X is a ___________ random
variable.
discrete
negative
continuous
positive
