Question

question #12
a statistics student is conducting an experiment where they roll a six - sided die and record the number that shows. the student got the die to land on 6 two times in a row.
is there enough statistical evidence to support the claim that the die is somehow rigged?
no, because the results are likely to happen by chance.
no, because the results are unlikely to happen by chance.
yes, because the results are likely to happen by chance.
yes, because the results are unlikely to happen by chance.
question #13
a teacher surveyed his students to determine how many siblings each student had. identify the type of data.
quantitative data
categorical data
continuous data
bimodal data

Explanation:

Question #12

When rolling a fair six - sided die, the probability of getting a 6 on a single roll is \(p=\frac{1}{6}\). The probability of getting a 6 two times in a row is \(P = \frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\approx0.0278\). While this is an unlikely event (since the probability is relatively low), getting a 6 two times in a row is still a possible outcome by chance. In statistics, for a claim of something being "rigged" (a significant deviation from the expected probability), more extensive evidence (like many more trials showing a consistent deviation) is usually required. Just two consecutive 6s is not enough to conclude the die is rigged as it can happen by chance.

Quantitative data is numerical data that represents a quantity. The number of siblings is a numerical value (e.g., 0, 1, 2, etc.). Categorical data is non - numerical and represents categories (e.g., gender: male/female). Continuous data can take any value within a range (e.g., height can be 1.5 m, 1.51 m, etc.), while the number of siblings is a discrete quantity (you can't have 1.5 siblings). Bimodal data refers to data with two modes (most frequently occurring values), which is a characteristic of a data distribution, not the type of data itself. Since the number of siblings is a numerical count, it is quantitative data.

Answer:

No, because the results are likely to happen by chance.

Question #13