# Answers to the checkpoints of chapter 4

**Checkpoint 1**

- Subjective probability.
- Relative probability.
- Probability of knowing.
- Probability of drawing a king: 4/52, probability of drawing a king of diamonds: 1/52.

**Checkpoint 2**

- 93%
- 0.0049
- 0.0651
- Three emergency calls are not independent; they probably concern the same incident. They are too close together and from the same suburb.

**Checkpoint 3**

- Both indicate the number of possible variations of a number of elements from a set. If it is a permutation, the order is taken into account. If it is a combination, it is not.
- Number of combinations: 6 choose 2 = 15

Number of permutations 6*5 = 30

**Checkpoint 4**

- It is a probability distribution with replacement, whereby the probabilities occur independently of each other.
- Hypergeometric = with replacement; binomial = without replacement.
- He can check this by doing a hypergeometric probability experiment.
- He would now use a binomial probability experiment.
- The expected value is the expected result of an experiment if the result is not known.

**Checkpoint 5**

- A normal probability experiment has a continuous distribution; hypergeometric and binomial probability distributions have a discrete distribution.
- When you do a transformation, you standardize the values according to the
*z*scale and make it possible to compare variables with different scales. - In both distributions, the figure is bell shaped, and in both distributions the empirical rule applies (as does Chebyshev’s rule). The difference is that in a standard normal distribution the mean is “0” and the standard deviation it is “1” because it has been transformed according to the
*z*distribution.

**Checkpoint 6**

Repeatability as a condition for the reliability of results.

**Checkpoint 7**

- The
*p*value represents the probability value: the probability of a certain event, given some basic data. - The difference between the right and left probability value has to do with the area where the
*z*value is located: right or left of the center of the distribution. - The probability value is slightly more than 5%; the chance that the manufacturer would adjust his machines at this value is small.