Probability Distributions: Master the Basics for Nursing Statistics

Question 1

Which of the following is a defining characteristic of the normal distribution?

Accepted Answer

Symmetrical bell-shaped curve with values extending to infinity in both directions

Answer

Mean, median, and mode are equal

Answer

Probability distribution is determined by the mean and standard deviation

Answer

Values are discrete

Question 2

The cumulative distribution function (CDF) of a probability distribution provides the:

Accepted Answer

Probability of observing a value less than or equal to a given threshold

Answer

Probability density at a given value

Answer

Variance of the distribution

Answer

Mean of the distribution

Question 3

The expected value of a random variable represents:

Accepted Answer

The average value of the random variable over many trials

Answer

The most likely value of the random variable

Answer

The standard deviation of the random variable

Answer

The variance of the random variable

Question 4

When using the normal distribution to approximate the binomial distribution, why is it crucial to ensure large sample sizes and small probabilities?

Accepted Answer

Both large sample sizes and small probabilities are required for the normal approximation to accurately represent the binomial distribution.

Answer

The normal distribution is always more accurate than the binomial distribution.

Answer

Small probabilities alone ensure the normal distribution is an appropriate approximation for discrete data.

Question 5

Which of these characteristics describes a normal distribution?

Accepted Answer

Symmetrical

Answer

Discrete

Answer

Right-skewed

Question 6

A medical researcher is testing a new drug with a success rate of 75%. What is the probability of a patient NOT receiving a positive outcome from the drug on the first attempt?

Accepted Answer

0.25

Answer

0.50

Answer

0.75

Answer

1

Question 7

Which of the following is the expected value of a discrete probability distribution?

Accepted Answer

The sum of all possible outcomes multiplied by their respective probabilities.

Answer

The average of all possible outcomes.

Answer

The most likely outcome.

Answer

The least likely outcome.

Question 8

A certain medical test has a sensitivity of 85% and a specificity of 90%. If the prevalence of the disease in the population is 15%, what is the positive predictive value of the test?

Accepted Answer

0.68

Answer

0.75

Answer

0.85

Answer

0.90

Question 9

Which distribution is characterized by its symmetrical, bell-shaped curve?

Accepted Answer

Normal distribution

Answer

Skewed to the right

Answer

Skewed to the left

Answer

Uniform distribution

Question 10

Which distribution models the occurrence of events within a fixed interval or space?

Accepted Answer

Poisson distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Uniform distribution

Question 11

What is the standard error of the mean for a sample of size 100 with a standard deviation of 5?

Accepted Answer

0.5

Answer

5

Answer

50

Answer

100

Question 12

According to the central limit theorem, which phenomenon occurs?

Accepted Answer

The distribution of sample means approaches the normal distribution as sample size increases

Answer

The sample mean is always equal to the population mean

Answer

It applies only to small sample sizes

Answer

It applies only to large sample sizes

Question 13

When rolling a fair six-sided die, what is the probability of landing on the number 6?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/12

Question 14

What is the probability of obtaining exactly 5 successes in 10 independent trials, each with a 0.5 probability of success?

Accepted Answer

0.258

Answer

0.025

Answer

0.101

Answer

0.512

Question 15

Which of the following is NOT a defining characteristic of a normal distribution?

Accepted Answer

Constant coefficient of variation

Answer

Bell-shaped curve

Answer

Symmetrical around the mean

Answer

Unimodal

Question 16

Which of the following probability distributions is appropriate for modeling the number of successes in a sequence of independent experiments with a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 17

Which method is used to calculate the probability of an event based on known or assumed facts or principles?

Accepted Answer

Theoretical method

Answer

Empirical method

Answer

Subjective method

Answer

Historical method

Question 18

A nurse is administering a medication to a patient. The effectiveness of the medication is estimated to be 75%. What is the probability that the medication will be ineffective?

Accepted Answer

0.25

Answer

0.50

Answer

0.75

Answer

1.00

Question 19

Which characteristic is NOT associated with a normal distribution?

Accepted Answer

Area under the curve is less than 1

Answer

Bell-shaped curve

Answer

Symmetry around the mean

Answer

Equality of mean, median, and mode

Question 20

Which of the following is NOT a practical application of probability distributions in nursing?

Accepted Answer

Making definitive diagnoses

Answer

Predicting patient outcomes

Answer

Assessing intervention effectiveness

Answer

Estimating complication risks

Question 21

In a population with a mean weight of 150 pounds and a standard deviation of 20 pounds, what is the probability of selecting a patient weighing less than 130 pounds?

Accepted Answer

0.0228

Answer

0.1587

Answer

0.8413

Answer

0.9772

Question 22

A nurse is analyzing the distribution of blood pressure readings in healthy adults. Which probability distribution is most suitable for modeling this data?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 23

Which statistical tool is used to visually represent the distribution of data?

Accepted Answer

Histogram

Answer

Scatterplot

Answer

Pie chart

Answer

Line graph

Question 24

What is a key characteristic of the normal distribution?

Accepted Answer

It is symmetrical around the mean.

Answer

It is skewed towards higher values.

Answer

It represents discrete probabilities.

Question 25

Which of the following is a characteristic of a normal distribution?

Accepted Answer

Symmetrical

Answer

Skewed

Answer

Rectangular

Answer

Bimodal

Question 26

A nurse is analyzing the number of patients admitted to the emergency department per hour. Which probability distribution is appropriate for this scenario?

Accepted Answer

Poisson distribution

Answer

Normal distribution

Answer

Binomial distribution

Question 27

Which of the following is a key assumption of the normal distribution?

Accepted Answer

Data is continuous

Answer

Population variance is known

Answer

Data is categorical

Answer

Sample size is very large

Question 28

Which of the following is a benefit of using probability distributions in nursing?

Accepted Answer

Making informed decisions

Answer

Eliminating all uncertainty in patient care

Answer

Ensuring all patient data is normally distributed

Answer

Predicting patient outcomes with certainty

Question 29

Which of the following is true about the standard deviation in a probability distribution?

Accepted Answer

It measures the spread of the data

Answer

It can be negative

Answer

It is affected by the sample size

Answer

It represents the mean of the data

Question 30

A nurse is concerned about the number of falls among elderly patients. Which probability distribution would be most appropriate for modeling the number of falls per week?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Question 31

Which characteristic is NOT associated with a normal distribution?

Accepted Answer

Skewness

Answer

Bell-shaped curve

Answer

Equal mean, median, and mode

Question 32

In a fair coin toss, what is the probability of obtaining exactly 5 heads in a row?

Accepted Answer

0.03125

Answer

0.125

Answer

0.25

Answer

0.5

Question 33

In a normal distribution with μ = 10 and σ = 2, what is the median?

Accepted Answer

10

Answer

12

Answer

8

Question 34

Which distribution is suitable for modeling the number of defects in a manufactured product?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Log-normal distribution

Answer

Normal distribution

Question 35

Which probability distribution describes the number of successes in a series of trials where two possible outcomes are equally likely and each trial is independent of the others?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 36

A nurse wants to analyze the frequency of patient falls in a hospital unit. Which probability distribution would be most appropriate for this situation?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Question 37

Which characteristic is unique to the normal distribution?

Accepted Answer

It is bell-shaped and symmetric around the mean.

Answer

It is bimodal.

Answer

It is skewed to the right.

Answer

It is only defined for positive values.

Question 38

What does the standard deviation of a probability distribution indicate?

Accepted Answer

How spread out the data is from the mean.

Answer

The average distance between data points

Answer

The total variability of the data

Answer

The probability of getting a specific value

Question 39

Which parameter of a probability distribution describes its central tendency?

Accepted Answer

Mean

Answer

Kurtosis

Answer

Skewness

Answer

Variance

Question 40

How can probability distributions be utilized in nursing practice?

Accepted Answer

Predicting patient outcomes and making informed decisions.

Answer

Performing surgical procedures

Answer

Diagnosing diseases with certainty

Answer

Prescribing specific medications

Question 41

Which measure quantifies the dispersion of data in a probability distribution?

Accepted Answer

Standard deviation

Answer

Median

Answer

Mean

Answer

Mode

Question 42

Which factor does NOT influence the shape of a probability distribution?

Accepted Answer

Data collection method

Answer

Skewness

Answer

Kurtosis

Answer

Central tendency

Question 43

A hospital is evaluating the length of stay for patients in the intensive care unit (ICU). The length of stay follows a normal distribution with a mean of 5 days and a standard deviation of 1.5 days. What is the probability that a patient will stay in the ICU for more than 7 days?

Accepted Answer

0.1587

Answer

0.3413

Answer

0.6827

Question 44

A nurse is assessing the risk of a patient developing a surgical site infection (SSI). The probability of developing an SSI is 0.05. What is the probability that the patient will NOT develop an SSI?

Accepted Answer

0.95

Answer

0.50

Answer

0.25

Answer

0.05

Question 45

The number of falls per month in a nursing home follows a normal distribution with a mean of 5 falls and a standard deviation of 2 falls. What is the probability that the nursing home will have fewer than 2 falls next month?

Accepted Answer

0.0548

Answer

0.2743

Answer

0.6915

Answer

0.9332

Question 46

A nurse is calculating the probability of a patient recovering from surgery. The probability of recovery is 0.8. What is the probability that the patient will NOT recover from surgery?

Accepted Answer

0.2

Answer

0.8

Answer

0.25

Answer

0.5

Question 47

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

Asymmetrical about the mean

Answer

Mean, median, and mode are equal

Answer

Bell-shaped

Answer

Found in nature and social sciences

Question 48

Which of the following is a measure of central tendency and can be calculated as the sum of all values divided by the number of values in a dataset?

Accepted Answer

Mean

Answer

Skewness

Answer

Standard deviation

Answer

Range

Question 49

Which of the following is a characteristic of a skewed distribution?

Accepted Answer

Not symmetrical about the mean

Answer

Bell-shaped

Answer

Found in nature and social sciences

Answer

Mean, median, and mode are equal

Question 50

A nurse is studying the number of patients admitted to the emergency room each hour. Which probability distribution is most appropriate for modeling this scenario?

Accepted Answer

Poisson distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Uniform distribution

Question 51

A study found that 70% of patients with a certain condition experience a positive response to a new medication. If 10 patients are randomly selected, what is the probability that exactly 6 will experience a positive response?

Accepted Answer

0.2001

Answer

0.5000

Answer

0.9000

Answer

0.7000

Question 52

The average weight of newborn babies at a hospital is 7.5 pounds with a standard deviation of 1.2 pounds. Assuming the weights are normally distributed, what is the probability of a newborn weighing between 6.3 and 8.7 pounds?

Accepted Answer

68.27%

Answer

34.13%

Answer

95.45%

Answer

99.73%

Question 53

A nurse is tracking the number of times a particular medical device malfunctions per day. What is the mean of the Poisson distribution in this scenario?

Accepted Answer

The average number of malfunctions per day

Answer

The probability of a malfunction

Answer

The number of days with malfunctions

Answer

The total number of malfunctions

Question 54

A researcher wants to determine if a new treatment is effective in reducing the incidence of a specific complication after surgery. Which type of probability distribution would be most appropriate for analyzing the data?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 55

The average number of patients admitted to the ICU each day is 5. What is the probability that on a particular day, more than 7 patients will be admitted to the ICU?

Accepted Answer

It can be calculated using the Poisson distribution with a mean of 5.

Answer

It can be calculated using the binomial distribution with a mean of 5.

Answer

It can be calculated using the normal distribution with a mean of 5.

Question 56

A blood pressure reading is considered high if it is above 140/90 mmHg. Assuming blood pressure follows a normal distribution with a mean of 120/80 mmHg and a standard deviation of 10/5 mmHg, what percentage of readings would be considered high?

Accepted Answer

This can be calculated using the standard normal distribution.

Answer

This can be calculated using the Poisson distribution.

Answer

This can be calculated using the binomial distribution.

Question 57

A nurse is administering a new medication to a group of patients. What is the probability that exactly 3 out of 10 patients will experience a specific side effect, given that the probability of experiencing the side effect is 15%?

Accepted Answer

This can be calculated using the binomial distribution.

Answer

This can be calculated using the normal distribution.

Answer

This can be calculated using the Poisson distribution.

Question 58

Which of the following is NOT a characteristic of the normal distribution?

Accepted Answer

The mean, median, and mode are always equal.

Answer

The distribution is bell-shaped and symmetrical.

Answer

The distribution is continuous.

Answer

The area under the curve represents the total probability.

Question 59

A researcher is studying the number of times a specific type of medical equipment is used per week. What is the standard deviation of the Poisson distribution in this scenario?

Accepted Answer

The square root of the mean

Answer

The variance

Answer

The mean itself

Answer

The probability of an event