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Probability Distribution Functions -Practice quiz

Total questions: 20

Worksheet time: 17mins

Name
Class
Date
1.



(a)  

2.

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)  

3.

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)  

4.

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)  

5.

Can the function in the given table be a probability distribution function?

a)

Yes, because all the probabilities are between 0 and 1

b)

No, because the sum of the probabilities is not 1

c)

Yes, because the sum of the probabilities is 1

d)

Yes, because it is in a table format.

e)

No, because some probabilities are less than zero.

6.

The function in the given table is a probability distribution function of a discrete random variable 𝑋. Find the value of 𝑎.

a)

12\frac{1}{2}  

b)

710\frac{7}{10}  

c)

310\frac{3}{10}  

d)

110\frac{1}{10}  

e)

25\frac{2}{5}  

7.

Write your answer as a fraction in its simplest form. use the / symbol e.g. 1/3

(a)  

8.

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)  

9.

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)  

10.

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)  

11.

Let X be the number of heads obtained when tossing

a fair coin 3 times.

What are the possible values of X?

a)

0,1,2,3,

b)

1,2,3,

c)

0,1,2,3,4

d)

1,2,3,4

12.

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?

a)

0,1,2,3,4,5

b)

1,2,3,4,5

c)

0,1,2,3,4

d)

1,2,3,4

13.

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)  

14.

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)  

15.

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)  

16.

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)  

17.

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)  

18.

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)  

19.

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)  

20.

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.

a)

discrete

b)

negative

c)

continuous

d)

positive