Statistical Reasoning - Probability Models

A set of flashcards covering key concepts and details related to probability models and statistical reasoning.

What is a probability model?

A mathematical representation of a random phenomenon that describes all possible outcomes and assigns probabilities to them.

What are the possible marital status outcomes for women aged 25 to 29 in the probability model?

Never Married, Married, Widowed, Divorced.

How is the probability of 'not married' calculated?

P(not married) = P(never married) + P(widowed) + P(divorced) = 0.478 + 0.004 + 0.042 = 0.524.

What does the complement of an event include?

All outcomes not in the event of interest.

How is the complement of an event A denoted?

A’ (A prime).

According to the rules of probability, what must the sum of the probabilities for all possible outcomes equal?

1.

What is the relationship between events that are mutually exclusive?

The probability that one or the other occurs is the sum of their individual probabilities.

What are the odds in relation to probability?

The ratio of the probability of an event happening to the probability of it not happening.

How would you calculate the probability of the New England Patriots winning based on given odds of 6 to 1?

The probability of losing is 6/(6 + 1) = 6/7 and the probability of winning is 1/(6 + 1) = 1/7.

What does the 68–95–99.7 rule state about normal distributions?

95% of all samples will give a sample proportion falling within 2 standard deviations of the mean.

What was the mean proportion when surveying about childhood vaccinations?

0.710.

What is the standard deviation of the sample proportions in the normal distribution discussed?

About 0.014.

For the given normal distribution of sample proportions, what is the probability that between 68.2% and 73.8% will say 'Yes'?

0.95.