A stem-and-leaf plot for the numbers of touchdowns scored by...

Name: Problem 75, Chapter 3: Elementary Statistics: Picturing the World
Uploaded: 2021-01-09T20:10:44-08:00
Duration: 5 min 19 s
Channel: Evelyn Cunningham
Description: A stem-and-leaf plot for the numbers of touchdowns scored by all 120 NCAA Division I Football Bowl Subdivision teams is shown. Find the probability that a team chosen at random scored (a) at least 51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than 72 touchdowns. Are any of these events unusual? Explain.

A stem-and-leaf plot for the numbers of touchdowns scored by all 120 NCAA Division I Football Bowl Subdivision teams is shown. Find the probability that a team chosen at random scored (a) at least 51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than 72 touchdowns. Are any of these events unusual? Explain.

A stem-and-leaf plot for the numbers of touchdowns scored by all 120 NCAA Division I Football Bowl Subdivision teams is shown. Find the probability that a team chosen at random scored (a) at least
51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than 72 touchdowns. Are any of these events unusual? Explain.

Key Concepts

Stem?and?Leaf Plot

A stem?and?leaf plot is a method of displaying numerical data where each data point is split into a 'stem' (usually representing the leading digit(s)) and a 'leaf' (usually representing the final digit). It helps in organizing and visualizing data distributions while preserving the actual data values.

Counting Techniques

Counting techniques involve systematically identifying the number of favorable outcomes for a defined event within a dataset. This is crucial when determining probabilities from data representations, such as locating specific data values in a stem?and?leaf plot.

Probability

Probability is the measure of how likely an event is to occur, calculated as the ratio of the number of favorable outcomes to the total number of outcomes. It provides a numerical quantification of uncertainty based on the available data.

Interpretation of Unusual Events

Interpreting unusual events in probability involves comparing the likelihood of the event to a threshold, often considering events with very low probabilities (for instance, less than 5%) as unusual. This concept helps in assessing whether a given outcome is statistically significant or rare.

Transcript

00:01 All right, this stem and leaf plot represents the number of touchdowns scored by all 120 ncaa division i football subdivision teams.

00:22 And we want to determine the probability that if we selected a team at random, that team, part a, scored at least 51 touchdowns.

00:36 So at least 51 could be translated into the probability that x is greater than are equal to 51.

00:44 Part b, we want the probability that randomly selected team scored between 20 and 30 touchdowns.

00:56 So that could be translated into the probability of 20, which is less than x, which is less than 30.

01:03 And for part c, we want the probability that the randomly selected team scored more than 72 touchdowns.

01:14 So i want you to keep in mind that probability is found by comparing the favorable over the possible.

01:26 So when we are looking for the probability of selecting a team that scored more than 51 touchdowns, or greater than or equal to, that would be all of these, all of these, all of these, all of these, and these.

01:46 So with the stem and leaf that represents eight, there's two teams there.

01:53 One team scored 84 touchdowns and another team scored 89 touchdown.

02:00 In the 70s, it represents six different teams.

02:05 In the 60s range, we're talking 20 different teams.

02:15 And the ones that would be classified as favorable in the 50s would be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 teams...

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