Table of contents

1. Intro to Stats and Collecting Data1h 14m

Intro to Stats
24m

Levels of Measurement
18m

Intro to Collecting Data
8m

Sampling Methods
23m

2. Describing Data with Tables and Graphs1h 55m

Visualizing Qualitative vs. Quantitative Data
4m

Frequency Distributions
35m

Histograms
14m

Bar Graphs and Pareto Charts
11m

Pie Charts
8m

Frequency Polygons
10m

Dot Plots
6m

Stemplots (Stem-and-Leaf Plots)
13m

Time-Series Graph
9m

3. Describing Data Numerically2h 5m

Mean
9m

Median
17m

Mode
7m

Standard Deviation
16m

Interpreting Standard Deviation
20m

Percentiles & Quartiles
14m

Describing Data Numerically Using a Graphing Calculator
10m

Boxplots
8m

Descriptive Statistics-Excel
11m

Boxplots-Excel
8m

4. Probability2h 16m

Basic Concepts of Probability
7m

Complements
6m

Addition Rule
17m

Multiplication Rule: Independent Events
11m

Introduction to Contingency Tables
17m

Multiplication Rule: Dependent Events
15m

Bayes' Theorem
13m

Fundamental Counting Principle
8m

Counting
37m

5. Binomial Distribution & Discrete Random Variables3h 6m

Discrete Random Variables
31m

Binomial Distribution
1h 7m

Finding Binomial Probabilities-Excel
17m

Poisson Distribution
40m

Finding Poisson Probabilities-Excel
15m

Hypergeometric Distribution
14m

6. Normal Distribution and Continuous Random Variables2h 11m

Uniform Distribution
18m

Standard Normal Distribution
39m

Probabilities & Z-Scores w/ Graphing Calculator
19m

Non-Standard Normal Distribution
21m

Finding Probabilities, Z Values, and X Values with the Normal Distribution-Excel
32m

7. Sampling Distributions & Confidence Intervals: Mean3h 23m

Sampling Distribution of the Sample Mean and Central Limit Theorem
19m

Distribution of Sample Mean - Excel
23m

Introduction to Confidence Intervals
15m

Confidence Intervals for Population Mean
1h 18m

Determining the Minimum Sample Size Required
12m

Finding Probabilities and T Critical Values - Excel
28m

Confidence Intervals for Population Means - Excel
25m

8. Sampling Distributions & Confidence Intervals: Proportion1h 25m

Sampling Distribution of Sample Proportion
29m

Confidence Intervals for Population Proportion
42m

Confidence Intervals for Population Proportion - Excel
12m

9. Hypothesis Testing for One Sample3h 29m

Steps in Hypothesis Testing
1h 1m

Performing Hypothesis Tests: Means
51m

Hypothesis Testing: Means - Excel
42m

Performing Hypothesis Tests: Proportions
27m

Hypothesis Testing: Proportions - Excel
27m

10. Hypothesis Testing for Two Samples4h 50m

Two Proportions
1h 13m

Two Proportions Hypothesis Test - Excel
28m

Two Means - Unknown, Unequal Variance
1h 3m

Two Means - Unknown Variances Hypothesis Test - Excel
12m

Two Means - Unknown, Equal Variance
15m

Two Means - Unknown, Equal Variances Hypothesis Test - Excel
9m

Two Means - Known Variance
12m

Two Means - Sigma Known Hypothesis Test - Excel
21m

Two Means - Matched Pairs (Dependent Samples)
42m

Matched Pairs Hypothesis Test - Excel
12m

11. Correlation1h 24m

Scatterplots & Intro to Correlation
26m

Correlation Coefficient
21m

Creating Scatterplots and FInding Correlation Coefficient - Excel
6m

Hypothesis Tests for Correlation Coefficient Using TI-84
17m

Inferences for the Correlation Coefficient - Excel
11m

12. Regression1h 50m

Linear Regression & Least Squares Method
26m

Residuals
12m

Coefficient of Determination
12m

Inferences for Slope
31m

Prediction Intervals
13m

Quadratic Regression
15m

13. Chi-Square Tests & Goodness of Fit2h 21m

Goodness of Fit Test
41m

Goodness of FIt Test Using TI-84
17m

Goodness of Fit Test - Excel
10m

Contingency Tables
12m

Independence Tests
14m

Homogeneity Tests
11m

Using Matrices on a TI-84
6m

Independence Test Using TI-84
12m

Independence Tests - Excel
13m

14. ANOVA1h 57m

Introduction to ANOVA
30m

Multiple Comparisons: Tukey Test
14m

Multiple Comparisons: Tukey-Kramer Test
15m

Multiple Comparisons: Bonferoni Test
24m

Two-Way ANOVA
32m

6. Normal Distribution and Continuous Random Variables

Uniform Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Uniform Distribution

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Multiple Choice

Shade the area corresponding to the probability listed, then find the probability.
$P of open paren X is less than 7.5 close paren$

Graph showing a shaded area under a uniform distribution curve, indicating P(X<7.5) with axes labeled for probability density and x. ; $P of open paren X is less than 7.5 close paren equals 0.15$

Graph showing a uniform distribution with shaded area representing P(X<7.5) under the probability density curve. ; $P of open paren X is less than 7.5 close paren equals 0.25$

Graph showing a uniform distribution with shaded area representing P(X<7.5) under the probability density curve. ; $P of open paren X is less than 7.5 close paren equals 0.5625$

Graph showing a shaded area under a uniform distribution curve, indicating P(X<7.5) with axes labeled for probability density and x. ; $P of open paren X is less than 7.5 close paren equals 0.5625$

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Verified step by step guidance

Step 1: Identify the type of distribution represented in the graph. The graph shows a triangular probability density function (PDF), which is a continuous distribution. The area under the curve represents probabilities.

Step 2: Recognize that the problem asks for the probability P(X < 7.5). This corresponds to the shaded area under the curve from the start of the distribution (x = 2.5) to x = 7.5.

Step 3: Break the shaded area into geometric shapes for calculation. The shaded region forms a triangle. The base of the triangle is from x = 2.5 to x = 7.5, and the height is determined by the value of the PDF at x = 7.5.

Step 4: Use the formula for the area of a triangle: Area = (1/2) × base × height. The base is (7.5 - 2.5 = 5), and the height is the value of the PDF at x = 7.5, which is 0.15.

Step 5: Calculate the area using the formula. This area represents the probability P(X < 7.5). Substitute the values into the formula to find the probability.