Deck 4: Discrete Probability Distributions

Question 1

Use the following distribution for the next questions. A graduate student in
exercise science surveyed undergraduate students' weekly exercise habits. The
following distribution gives the probability values for x, the number of days an
undergraduate student exercised per week.
Identify the random variable for the exercise science distribution.

Answer 1

The number of days an undergraduate student exercised per week

Question 2

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Find the mean of the proba bility distribution for offspring of Accipiter spp.

Answer 2

2.5 offspring

Question 3

Use the following binomial distribution for the next questions. A doctor knows
from experience that 10% of the patients to whom she gives a certain medication
will experience undesirable side effects. Assume the doctor gives medication to the
next 12 patients.
Find the mean from the binomial distribution for the medication.

Answer 3

1.2 patients

Question 4

Use the following Poisson distribution for the next questions. For a science
laboratory experiment, the average number of radioactive particles passing
through a counter in a millisecond is four.
Find the probability that at most three particles pass through the counter in a given millisecond.

Question 5

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Using probability values, determine if it is unusual for Accipiter spp. to have six offspring.

Question 6

Use the following binomial distribution for the next questions. A doctor knows
from experience that 10% of the patients to whom she gives a certain medication
will experience undesirable side effects. Assume the doctor gives medication to the
next 12 patients.
Referring to the binomial distribution for the medication, find the probability that exactly five of these patients will experience undesirable side effects.

Question 7

Use the following binomial distribution for the next questions. A doctor knows
from experience that 10% of the patients to whom she gives a certain medication
will experience undesirable side effects. Assume the doctor gives medication to the
next 12 patients.
Referring to the binomial distribution for the medication, find the probability that exactly three of these patients will experience undesirable side effects.

Question 8

Use the following binomial distribution for the next questions. A doctor knows
from experience that 10% of the patients to whom she gives a certain medication
will experience undesirable side effects. Assume the doctor gives medication to the
next 12 patients.
Find the standard deviation from the binomial distribution for the medication.

Question 9

Use the following distribution for the next questions. A graduate student in
exercise science surveyed undergraduate students' weekly exercise habits. The
following distribution gives the probability values for x, the number of days an
undergraduate student exercised per week.
Determine whether a probability distribution is given in the exercise science distribution. If not, identify the requirements that are not satisfied.

Question 10

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Referring to the probability distribution for offspring of Accipiter spp., find the probability of having exactly three offspring.

Question 11

Use the following distribution for the next questions. A graduate student in
exercise science surveyed undergraduate students' weekly exercise habits. The
following distribution gives the probability values for x, the number of days an
undergraduate student exercised per week.
Identify the random variable as either discrete or continuous.

Question 12

Select the procedure that does NOT result in a Poisson distribution.

A) Researching the Northern Spotted Owls' number of feedings per month
B) Researching the Barred Owls' wingspan in inches
C) Researching the Snowy Owls' number of migrations over 20 years
D) Researching the number of Sooty Owls' deaths per year SHORT ANSWER. Using the following information, write the word, phrase, or
Value that best answers the problem.
Use the following binomial distribution for the next six questions. A doctor knows
From experience that 10% of the patients to whom she gives a certain medication
Will experience undesirable side effects. Assume the doctor gives medication to the
Next 12 patients.

Question 13

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Find the Expected Value of the probability distribution for offspring of Accipiter spp.

Question 14

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Find the standard deviation of the probability distribution for offspring of Accipiter spp.

Question 15

Use the following distribution for the next questions. A statistics student
surveyed the probabilities for x, the number of classmates who were not paying
attention to the lecture.
Identify the random variable for the statistics class distribution.

Question 16

Select the procedure that does NOT result in a binomial distribution.

A) Surveying dental patients and asking them if they experienced anxiety during their appointment
B) Surveying dental patients and asking them if they did or did not floss before their appointment
C) Surveying dental patients and asking them if they have dental insurance
D) Surveying dental patients and asking them how their teeth feel after their appointment

Question 17

Use the following binomial distribution for the next questions. A doctor knows
from experience that 10% of the patients to whom she gives a certain medication
will experience undesirable side effects. Assume the doctor gives medication to the
next 12 patients.
Referring to the binomial distribution for the medication, find the probability that at most two of these patients will experience undesirable side effects.

Question 18

Use the following Poisson distribution for the next questions. For a science
laboratory experiment, the average number of radioactive particles passing
through a counter in a millisecond is four.
Find the probability that no particles pass through the counter in a given millisecond.

Question 19

Use the following Poisson distribution for the next questions. For a science
laboratory experiment, the average number of radioactive particles passing
through a counter in a millisecond is four.
Find the probability that six particles pass through the counter in a given millisecond.

Question 20

Use the following probability distribution for the next questions. Biologists
researching a certain type of hawk, Accipiter spp., found the following probability
values for x, the number of offspring.
Referring to the probability distribution for offspring of Accipiter spp., find the probability of having more than three offspring.

Question 21

Use the following distribution for the next questions. A statistics student
surveyed the probabilities for x, the number of classmates who were not paying
attention to the lecture.
Identify the random variable as either discrete or continuous.

Question 22

Use the following binomial distribution for the next questions. A scientist
knows that piñon jays that breed in captivity and are released have the ability to find 70% of caches, or hidden sources of food, in the wild. Assume the scientist releases 15 piñon jays.
Find the mean from the binomial distribution for the cache finding ability of these piñon jays.

Question 23

Use the following binomial distribution for the next questions. A scientist
knows that piñon jays that breed in captivity and are released have the ability to find 70% of caches, or hidden sources of food, in the wild. Assume the scientist releases 15 piñon jays.
Find the standard deviation from the binomial distribution for the cache-finding ability of these piñon jays.

Question 24

Use the following Poisson distribution for the next questions. An allergist determined the average number of fire ants per square centimeter of a mound is six
Find the probability that no fire ants are in a square centimeter of a mound.

Question 25

Use the following Poisson distribution for the next questions. An allergist determined the average number of fire ants per square centimeter of a mound is six
Find the probability of eight fire ants in a square centimeter of a mound.

Question 26

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Find the mean of the probability distribution for the age children begin brushing their teeth or gums.

Question 27

Select the procedure that does NOT result in a Poisson distribution.

A) Researching the Scarlet Snakes' number of feedings per month
B) Researching the number of bands on the Gray-banded Kingsnake
C) Researching the Racer Snakes' number of eggs laid over the breeding season
D) Researching the number of Mud Snakes' deaths per year

Question 28

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Referring to the probability distribution for dental habits of children, find the probability of a two-year-old beginning to brush their teeth or gums.

Question 29

Select the procedure that does NOT result in a binomial distribution.

A) Surveying cardiology patients and asking them if they experienced stress during their appointment
B) Surveying cardiology patients and asking them if they did or did not eat a bacon cheese hamburger before their appointment
C) Surveying cardiology patients and asking them if they have health insurance
D) Surveying cardiology patients and asking them how their heart feels after their appointment

Question 30

Use the following binomial distribution for the next questions. A scientist
knows that piñon jays that breed in captivity and are released have the ability to find 70% of caches, or hidden sources of food, in the wild. Assume the scientist releases 15 piñon jays.
Referring to the binomial distribution for the piñon jays, find the probability that exactly five of these birds will be able to find caches.

Question 31

Use the following binomial distribution for the next questions. A scientist
knows that piñon jays that breed in captivity and are released have the ability to find 70% of caches, or hidden sources of food, in the wild. Assume the scientist releases 15 piñon jays.
Referring to the binomial distribution for the piñon jays, find the probability that exactly 12 of these birds will be able to find caches.

Question 32

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Using probability values, determine if it is unusual for a child less than one year old to brush their teeth or gums.

Question 33

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Find the Expected Value of the probability distribution for the age children begin brushing their teeth or gums.

Question 34

Use the following Poisson distribution for the next questions. An allergist determined the average number of fire ants per square centimeter of a mound is six
Find the probability that at most four fire ants are in a square centimeter of a mound.

Question 35

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Referring to the probability distribution for dental habits of children, find the probability of a child three years old or older beginning to brush their teeth or gums.

Question 36

Use the following distribution for the next questions. A statistics student
surveyed the probabilities for x, the number of classmates who were not paying
attention to the lecture.
Determine whether a probability distribution is given in the statistics class distribution. If not, identify the requirements that are not satisfied.

Question 37

Use the following binomial distribution for the next questions. A scientist
knows that piñon jays that breed in captivity and are released have the ability to find 70% of caches, or hidden sources of food, in the wild. Assume the scientist releases 15 piñon jays.
Referring to the binomial distribution for the piñon jays, find the probability that at least 13 of these birds will be able to find caches.

Question 38

Use the following probability distribution for the next questions. Dental
researchers found the following probability values for the dental habits of x, the age children begin brushing their teeth or gums.

Find the standard deviation of the probability distribution for the age children begin brushing their teeth or gums.