Exam 2 Review Summary

Boxplots and Five-Number Summary

  • Boxplots represent distributions: one for men's weights, one for women's weights. The lower boxplot typically indicates women's weights.

  • For speed dating ratings, a constructed boxplot yields a five-number summary: 2.0, 6.1, 7.0, 8.0, 10.0.

Z-Scores and Statistical Analysis

  • Highest Verizon airport data speed of 77.8 Mbps (Atlanta):

    • Mean: i = 17.60 Mbps, Standard deviation: s = 16.02 Mbps.

    • Z-score for Atlanta's speed: z = 3.76.

  • Adult females' pulse rates: lowest 36 bpm, Mean: x = 74.0 bpm, Standard deviation: s = 12.5 bpm.

    • Z-score for 36 bpm: z = -3.04.

ACT Test Analysis

  • Mean ACT score: 21.1, Standard deviation: 5.1.

    • Significantly low scores < 12.4, significantly high scores > 31.3.

Coin Weights

  • Coin weights mean: 5.63930 g, standard deviation: 0.06194 g.

    • Identify significantly low (< 5.51542 g) or high (> 5.76318 g) weights.

Percentiles and Quartiles

  • For Sprint cell phone data speeds (Mbps):

    • 2.4 Mbps corresponds to 58th percentile.

    • 0.7 Mbps corresponds to 34th percentile.

Probability Concepts

  • Events and probabilities:

    • Random guesses: 50/50 (0.5) for true/false, 1/5 (0.2) for multiple-choice.

    • Typical response probabilities (e.g., luggage color, sleepwalking prevalence) noted.

    • Consider sample space for two births: {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}.

Probability Calculations

  • Complement probabilities and basic events:

    • Probability of a different seating for texting: P({not yes}) = 1 - 0.26 = 0.74.

Driver Behavior with Seatbelts

  • Drive-thru order statistics data:

    • Order Accuracy: McDonald's 329 accurate out of 1118 total orders

    • Probabilities: Overall, 0.676 not from McDonald's; 0.117 for not accurate orders; etc.

Dice Probability

  • Two six-sided dice: probabilities for various sums (odd/even, certain totals).

  • Evaluate events (disjoint or not) based on outcomes.

Random Variables and Distribution

  • Random variables defined, values enumerated.

  • Checks for probability distribution validity (sums, range of probabilities).