Free Throws A basketball player habitually makes 70 % of her...

Free Throws A basketball player habitually makes $70 \%$ of her free throws. In an experiment, a researcher asks this basketball player to record the number of free throws she shoots until she misses. The experiment is repeated 50 times. The following table lists the distribution of the number of free throws attempted until a miss is recorded. (a) Construct a relative frequency distribution of the data. (b) What percentage of the time did she miss on her fourth free throw? (c) What percentage of the time did she make nine in a row and then miss the tenth free throw? (d) What percentage of the time did she make at least five in a row? TABLE CANT COPY

Free Throws A basketball player habitually makes $70 \%$ of her free throws. In an experiment, a researcher asks this basketball player to record the number of free throws she shoots until she misses. The experiment is repeated 50 times. The following table lists the distribution of the number of free throws attempted until a miss is recorded.
(a) Construct a relative frequency distribution of the data.
(b) What percentage of the time did she miss on her fourth free throw?
(c) What percentage of the time did she make nine in a row and then miss the tenth free throw?
(d) What percentage of the time did she make at least five in a row?
TABLE CANT COPY

Key Concepts

Percentage Calculations in Experimental Data

Calculating percentages in experimental data often involves converting raw frequencies or computed probabilities into percentages. This is used to express how often a certain outcome occurs relative to total trials, thereby making the data easier to understand, compare, and interpret.

Geometric Distribution

The geometric distribution models the number of Bernoulli trials needed to achieve the first failure (or success, depending on the definition) in a sequence of independent trials. It is particularly useful for determining the probability of a result occurring at a specific trial number after a sequence of successes.

Multiplication Rule for Independent Events

The multiplication rule for independent events states that the probability of a series of independent events occurring consecutively is the product of their individual probabilities. This rule is essential when calculating the probability of a specific sequence of outcomes in repeated trials, such as making several free throws in a row followed by a miss.

Relative Frequency Distribution

A relative frequency distribution displays the proportion or percentage of observations that fall within each category relative to the total number of observations. Instead of using raw counts, each frequency is divided by the total number of trials, enabling easier comparison across different categories or experiments.

Bernoulli Trials

Bernoulli trials are a sequence of experiments where each trial has exactly two possible outcomes, typically called 'success' and 'failure'. Each trial is independent, and the probability of success remains constant throughout the experiment, which forms the basis for many discrete probability models.

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