Question 1

A hospital administrator wants to summarize the years nurses stay in their positions. The data collected are: 23, 2, 5, 14, 25, 36, 27, 42, 12, 8. Which of the following best describes the skewness of this data set?

Accepted Answer

The data is positively skewed (right-skewed).

Question 2

Given the nurse tenure data: 23, 2, 5, 14, 25, 36, 27, 42, 12, 8, what is the mean number of years nurses stay in their positions? Use the formula $$\bar{x} = \frac{\sum x_i}{n}.$$

Accepted Answer

$$\bar{x} = 19.4$$

Question 3

A researcher calculates the correlation coefficient $$r$$ between two variables and finds $$r = -0.88. $$What does this value indicate?

Accepted Answer

There is a strong negative linear relationship between the variables.

Question 4

Suppose the time to repair a vehicle at an auto shop is normally distributed with mean $$\mu = 102$$ minutes and standard deviation $$\sigma = 18$$ minutes. What percentage of jobs take between 66 and 120 minutes? (Use the empirical rule.)

Accepted Answer

Approximately 81.5% (from $$\mu - 2\sigma to$$ $$\mu + 1\sigma)$$

Question 5

If 300 vehicles are repaired at the shop, how many would you expect to take less than 66 minutes? (Assume normal distribution with $$\mu = 102$$, $$\sigma = 18.)$$

Accepted Answer

About 7 vehicles

Question 6

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of patients admitted to a hospital each day.

Question 7

A probability distribution is given as follows: $$P(X=1)=0.2$$, $$P(X=2)=0.3$$, $$P(X=3)=0.4$$, $$P(X=4)=0.1. Is $$this a valid probability distribution?

Accepted Answer

Yes, because the probabilities sum to 1.

Question 8

Given the probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.3$$, $$P(X=3)=0.4$$, $$P(X=4)=0.1$$, what is the expected value $$E(X)$$?

Accepted Answer

$$E(X) = 2.4$$

Question 9

Which of the following best describes the difference between a combination and a permutation?

Accepted Answer

A permutation considers order, while a combination does not.

Question 10

A researcher wants to select a sample of patients such that every patient has an equal chance of being chosen. Which sampling technique is being used?

Accepted Answer

Simple random sampling

Question 11

If you roll a fair 6-sided die and select a card from a deck labeled 1-10, what is the probability of rolling an even number and also drawing an even number? (Assume independence.)

Accepted Answer

$$P = \frac{1}{4}$$

Question 12

If there are 5 sets of colored plates (red, yellow, blue, green, black) and each set has 4 shapes (square, triangle, circle, oval), what is the probability of selecting a yellow or a triangular plate?

Accepted Answer

$$P = \frac{7}{20}$$

Question 13

Which of the following is an example of a continuous random variable?

Accepted Answer

The time it takes for a nurse to complete a shift.

Question 14

A probability distribution for the number of meals a student eats per day is given. How would you calculate the probability that a student has between 1 and 4 meals a day (inclusive)?

Accepted Answer

Add the probabilities for 1, 2, 3, and 4 meals.

Question 15

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time.

Question 16

A hospital records the number of days patients stay. Which level of measurement is this data?

Accepted Answer

Ratio

Question 17

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.8$$

Question 18

A nurse is selected at random from a hospital. If 60% are female and 40% are male, what is the probability that a randomly selected nurse is female, given that the nurse works the night shift and 70% of night shift nurses are female?

Accepted Answer

0.70

Question 19

Which of the following is the correct formula for the standard deviation of a sample?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Statistics Review: Chapters 1-4 Study Guidance

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