Statistics Chapter 6 - Continuous Probability Distributions

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Author:
honestkyle
ID:
207342
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Statistics Chapter 6 - Continuous Probability Distributions
Updated:
2013-04-11 12:16:01
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probability stats
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Continuous probability distributions
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  1. What does continuous mean?
    The number of possible real numbers in any interval is infinite.
  2. If a line represents an interval, and x can take on any real value along that line, then what?
    x is continuous
  3. If a line represents an interval, and x CAN'T take on any real value along that line, then what?
    x is discrete
  4. What is the probability that x is a specific value in a continuous distribution?
    • 1/
    • It can't be calculated
  5. Instead of calculating a specific value in a continuous probability distribution, what CAN we calculate?
    • x is inside an interval
  6. What does  represent?
    The area under the curve
  7. What does the area under the whole curve equal?
    1
  8. What are continuous probability distributions often referred to as?
    probability density functions
  9. Give some examples of where a normal probability distribution is used?
    • Heights of people
    • Scientific measurements
    • Test scores
    • Amount of rainfall
  10. Abraham De Moivre is known for what?
    • Derived the normal distribution
    • Predicted the date of his own death
  11. Carl F. Guass is known for what?
    Applied the normal distribution while studying motion of planets and stars
  12. What is the skewness of a normal probability distribution?
    0
  13. What is the highest point of a normal probability distribution?
    • Mean
    • mean = median = mode
  14. In a normal probability distribution what does the standard deviation determine?
    The spread
  15. What is a normal distribution commonly referred to as?
    Family of distributions
  16. What is p(x=a)?
    • 0
    • Can not be calculated
  17. What is the total area under the curve equal to ?
    1
  18. What is the area under the curve on one side of the mean?
    0.5
  19. What probability of values have a standard deviation > -2 and < 2?
    95.44%
  20. What probability of values have a standard deviation > -1 and < 1?
    68.26%
  21. What probability of values have a standard deviation > -3 and < 3?
    99.72%
  22. What is the z-score a measure of?
    The number of standard deviations x is from 
  23. What is the z-score equation?
  24. Linemen weigh an average of 300 lbs, with a std.dev. of 20 lbs. What is the probability that a randomly selected lineman will weigh 320 lobs or less?
    • Draw normal distribution curve
    • Right std.dev. = 320, 340, and 360
    • Left std.dev. = 280, 260, and 240
    • Look-up on z-score table, 1 = 0.8413
  25. Weight of college lineman:


    What is the probability that a randomly selected lineman will weigh at least 320 lbs?


    • z-score of 1 = 0.8413
    • 1-0.8413=0.1587
  26. Weight of lineman:


    What is the probability that a lineman will weigh between 320 and 330 lbs?
    • 320 = z-score of 1
    • 330 = z-score of 1.333
    • 0.9082 - 0.8413 = 0.0669
  27. The average IQ is 100 and the std.dev. is 15. What is the 95 percentile?
    • Look up 0.9500 (closest) on chart.
    • 0.9495 and 0.9505 are equal distance so take difference in z-scores = 1.654
    • x = 124.675

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