Question 1

The Poisson distribution describes the count X of random independent events over a fixed period of time or space.

Accepted Answer

A) True 
 B)False  True

Question 2

According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 8 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy.
Which distribution does X follow?

Accepted Answer

A) Normal distribution with mean 8 and variance 0.07 
B) Binomial distribution with n = 8 and p = 0.07 
C) Binomial distribution with n = 8 and p = 0.93 
D) Poisson distribution with mean and variance 0.07 
A) Normal distribution with mean 8 and variance 0.07 
B) Binomial distribution with n = 8 and p = 0.07 
C) Binomial distribution with n = 8 and p = 0.93 
D) Poisson distribution with mean and variance 0.07 B

Question 3

Patients with infections are randomly selected and the number of distinct species belonging to the Spirochaete phylum (responsible for illnesses such as Lyme disease and syphilis) are recorded. Let X count the number of distinct species found. It is speculated that X follows a Poisson distribution with a mean of 0.25.
What is the probability of observing someone with exactly zero distinct species?

Accepted Answer

A) 0.0000 
B) 0.2212 
C) 0.6065 
D) 0.7788 
A) 0.0000 
B) 0.2212 
C) 0.6065 
D) 0.7788 D

Question 4

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
If 500 births were observed rather than only 5, what is the approximate probability that at least 490 do not result in birth defects?

Accepted Answer

A) 0.0000 
B) 0.0901 
C) 0.6371 
D) 0.9105 
A) 0.0000 
B) 0.0901 
C) 0.6371 
D) 0.9105

Question 5

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
Which distribution does X follow?

Accepted Answer

A) Normal distribution with mean 5 and variance 1/33 
B) binomial distribution with n = 5 and p = 1/33 
C) binomial distribution with n = 5 and p = 32/33 
D) Normal distribution with mean 0 and variance 1 
A) Normal distribution with mean 5 and variance 1/33 
B) binomial distribution with n = 5 and p = 1/33 
C) binomial distribution with n = 5 and p = 32/33 
D) Normal distribution with mean 0 and variance 1

Question 6

Under which conditions can the Normal approximation to the binomial distribution be used?

Accepted Answer

A) n > 30 
B) np ≥10 and np(1-p) ≥10 
C) np ≥10 or np(1-p) ≥10 
D) None of these choices is correct. 
A) n > 30 
B) np ≥10 and np(1-p) ≥10 
C) np ≥10 or np(1-p) ≥10 
D) None of these choices is correct.

Question 7

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
What are the approximate mean and standard deviation of the distribution of X?

Accepted Answer

A) Mean = 0.1515 and standard deviation = 0.1469 
B) Mean = 4.8485 and standard deviation = 0.3833 
C) Mean = 0.1515 and standard deviation = 0.3833 
D) Mean = 4.8485 and standard deviation = 0.1469 
A) Mean = 0.1515 and standard deviation = 0.1469 
B) Mean = 4.8485 and standard deviation = 0.3833 
C) Mean = 0.1515 and standard deviation = 0.3833 
D) Mean = 4.8485 and standard deviation = 0.1469

Question 8

Patients with infections are randomly selected and the number of distinct species belonging to the Spirochaete phylum (responsible for illnesses such as Lyme disease and syphilis) are recorded. Let X count the number of distinct species found. It is speculated that X follows a Poisson distribution with a mean of 0.25.
What is the probability of observing a nonzero number of distinct species?

Accepted Answer

A) 0.2212 
B) 0.2500 
C) 0.5000 
D) 1.0000 
A) 0.2212 
B) 0.2500 
C) 0.5000 
D) 1.0000

Question 9

People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them.
What is the mean of X?

Accepted Answer

A) 7.2 
B) 1.44 
C) 1.34 
D) 0.072 
A) 7.2 
B) 1.44 
C) 1.34 
D) 0.072

Question 10

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York.
In this context, the probability P(X ≤ 1) is equal to which of these probabilities?

Accepted Answer

A) P(X = 1) 
B) P(X < 1) 
C) P(X < 2) 
D) P(X ≤ 2) 
A) P(X = 1) 
B) P(X < 1) 
C) P(X < 2) 
D) P(X ≤ 2)

Question 11

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent.
What is the probability of observing exactly zero emergency arrival?

Accepted Answer

A) Nearly 0 
B) 0.0082 
C) 0.1118 
D) 0.8230 
A) Nearly 0 
B) 0.0082 
C) 0.1118 
D) 0.8230

Question 12

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York.
Which distribution does X follow?

Accepted Answer

A) Poisson distribution with mean 29 
B) Poisson distribution with mean 14.5 
C) Binomial distribution with mean 0.145 
D) Binomial distribution with mean 2.9 
A) Poisson distribution with mean 29 
B) Poisson distribution with mean 14.5 
C) Binomial distribution with mean 0.145 
D) Binomial distribution with mean 2.9

Question 13

According to the National Institute of Allergy and Infectious Diseases, approximately 3.7% of U.S. adults have a food allergy. A large company plans a lunch reception for its 400 employees. Assume that employees are independent. Let the random variable X be the number of company employees who have a food allergy.
Which distribution does X follow?

Accepted Answer

A) Poisson distribution 
B) Binomial distribution 
C) Conditional distribution 
D) Uniform distribution 
A) Poisson distribution 
B) Binomial distribution 
C) Conditional distribution 
D) Uniform distribution

Question 14

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent.
What is the probability P(X < 3)?

Accepted Answer

A) Nearly 0 
B) 0.1425 
C) 0.1517 
D) 0.2942 
A) Nearly 0 
B) 0.1425 
C) 0.1517 
D) 0.2942

Question 15

According to the National Institute of Allergy and Infectious Diseases, approximately 3.7% of U.S. adults have a food allergy. A large company plans a lunch reception for its 400 employees. Assume that employees are independent. Let the random variable X be the number of company employees who have a food allergy.
What is the probability that none of the 400 employees has a food allergy?

Accepted Answer

A) Nearly 1 
B) 0.0370 
C) 0.0025 
D) Nearly 0 
A) Nearly 1 
B) 0.0370 
C) 0.0025 
D) Nearly 0

Question 16

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
What is the probability that at least one of the births results in a defect?

Accepted Answer

A) 0.0000 
B) 0.1426 
C) 0.8574 
D) 1.0000 
A) 0.0000 
B) 0.1426 
C) 0.8574 
D) 1.0000

Question 17

According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 8 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy.
What is the probability that one of the eight children has a food allergy?

Accepted Answer

A) 0.8965 
B) 0.3370 
C) 0.1250 
D) 0.0700 
A) 0.8965 
B) 0.3370 
C) 0.1250 
D) 0.0700

Question 18

People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them.
What is the standard deviation of X?

Accepted Answer

A) 1.16 
B) 1.20 
C) 1.34 
D) 1.44 
A) 1.16 
B) 1.20 
C) 1.34 
D) 1.44

Question 19

Patients with infections are randomly selected and the number of distinct species belonging to the Spirochaete phylum (responsible for illnesses such as Lyme disease and syphilis) are recorded. Let X count the number of distinct species found. It is speculated that X follows a Poisson distribution with a mean of 0.25.
What is the probability of observing exactly two distinct species?

Accepted Answer

A) 0.0000 
B) 0.0243 
C) 0.4631 
D) 0.9978 
A) 0.0000 
B) 0.0243 
C) 0.4631 
D) 0.9978

Question 20

According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or younger have a food allergy. A day care program has capacity for 8 children in that age range. Assume that the children attending the day care program are independent. Let the random variable X be the number of children in this day care who have a food allergy.
What is the probability that at least one of the eight children has a food allergy?

Accepted Answer

A) 0.8965 
B) 0.5596 
C) 0.4404 
D) 0.3370 
A) 0.8965 
B) 0.5596 
C) 0.4404 
D) 0.3370

The Poisson distribution describes the count X of random independent events over a fixed period of time or space.

Under which conditions can the Normal approximation to the binomial distribution be used?

People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them. What is the mean of X?

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York. In this context, the probability P(X ≤ 1) is equal to which of these probabilities?

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability of observing exactly zero emergency arrival?

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York. Which distribution does X follow?

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability P(X < 3)?

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Essential Probability Rules

Independence and Conditional Probabilities

The Normal Distributions

Sampling Distributions

Introduction to Inference

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

Filters

Exam 11: Discrete Probability Distributions

The Poisson distribution describes the count X of random independent events over a fixed period of time or space.

Under which conditions can the Normal approximation to the binomial distribution be used?

People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them. What is the mean of X?

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York. In this context, the probability P(X ≤ 1) is equal to which of these probabilities?

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability of observing exactly zero emergency arrival?

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York. Which distribution does X follow?

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability P(X < 3)?

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Essential Probability Rules

Independence and Conditional Probabilities

The Normal Distributions

Sampling Distributions

Introduction to Inference

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

Filters