Definition of probability, Binomial distribution, Normal distribution Poisson’s distribution, properties – problems . Mathematical / classical probability equation , The multiplicative law of probability when are not mutually exclusive, THE BINOMIAL DISTRIBUTION – with continuous data, The standard normal probability curve

1. Definition of probability, Binomial distribution,
Normal distribution, Poisson’s distribution,
properties – problems

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P r o b a b i l i t y
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3. Basic terminology
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P r o b a b i l i t y
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4. Basic terminology
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P r o b a b i l i t y
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5. Basic terminology
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P r o b a b i l i t y
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6. Mathematical / classical probability equation
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P r o b a b i l i t y
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7. Mathematical / classical probability equation
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P r o b a b i l i t y
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P r o b a b i l i t y
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Exercise

9. Exercise
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10. Exercise Probability Distribution for tablet attributes
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11. Exercise
Condition 2. If specked and chipped events are not mutually exclusive
equation is … P(A or B) = P(A) + P(B) - P(A and B)
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12. Exercise
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P r o b a b i l i t y
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13. Exercise Probability Distribution where attributes are not all mutually
exclusive.
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P r o b a b i l i t y
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14. Exercise
The multiplicative law of probability when are not mutually exclusive
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P r o b a b i l i t y
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P r o b a b i l i t y
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16. 1
P r o b a b i l i t y
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17. with discrete data
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B i n o m i a l D i s t r i b u t i o n

18. Example: the result of treatment with an antibiotic is that an infection is
either cured or not cured within five days.
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B i n o m i a l D i s t r i b u t i o n
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19. 1
Probability distribution of a binomial outcome based on a
single observation.
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B i n o m i a l D i s t r i b u t i o n

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B i n o m i a l D i s t r i b u t i o n

21. expansion of the expression:
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B i n o m i a l D i s t r i b u t i o n

22. expansion of the expression:
- For, the result of treatment with an antibiotic , p = 0.75 and q =0.25
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B i n o m i a l D i s t r i b u t i o n

23. expansion of the expression:
- Further expansion of equation
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B i n o m i a l D i s t r i b u t i o n

24. expansion of the expression:
- Consider the binomial distribution with p = 0.75 and N = 4 for the
antibiotic example.
- There are five possible outcomes
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B i n o m i a l D i s t r i b u t i o n

25. expansion of the expression:
1. no patients are cured X = 0
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B i n o m i a l D i s t r i b u t i o n

26. expansion of the expression:
2. three patients are cured X =3
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B i n o m i a l D i s t r i b u t i o n

27. 2
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B i n o m i a l D i s t r i b u t i o n

28. Exercise : Calculate the probability of one success in 100 trials if p =
0.01
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B i n o m i a l D i s t r i b u t i o n

29. THE BINOMIAL DISTRIBUTION – with continuous data
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B i n o m i a l D i s t r i b u t i o n

30. THE BINOMIAL DISTRIBUTION – with continuous data
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B i n o m i a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

32. 3
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N o r m a l D i s t r i b u t i o n

33. - As value of x increases numerically on either side of top (x= μ ), the
value of P(x) decreases rapidly
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N o r m a l D i s t r i b u t i o n

34. - The equation for the normal distribution (normal probability density)
- Where,
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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

38. - In this example, the histogram of tablet weights looks like a normal
curve.
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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

42. The standard normal probability curve has a
mean of 0 and a s.d. of 1
- The equation becomes..
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N o r m a l D i s t r i b u t i o n

43. The standard normal curve has a mean of 0 and a s.d. of 1
- a table of cumulative areas under the standard normal curve, giving
the area below Z.
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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

49. the Z transformation
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N o r m a l D i s t r i b u t i o n

50. Limits,
no tablet may differ from the average weight by more than 20%
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N o r m a l D i s t r i b u t i o n

51. the Z transformation less than 80.96mg and fining area using the Table
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N o r m a l D i s t r i b u t i o n

52. the Z transformation less than 121.44mg and fining area using the Table
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N o r m a l D i s t r i b u t i o n

53. the Z transformation
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N o r m a l D i s t r i b u t i o n

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N o r m a l D i s t r i b u t i o n

55. 5
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P o i s s o n D i s t r i b u t i o n

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P o i s s o n D i s t r i b u t i o n

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P o i s s o n D i s t r i b u t i o n

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P o i s s o n D i s t r i b u t i o n

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P o i s s o n D i s t r i b u t i o n

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P o i s s o n D i s t r i b u t i o n

61. 1. What is the probability that three of six patients will be cured if the
probability of a cure is 60%? Ans = 0.276
2. What is the probability of observing exactly one head in 10 tosses of
a coin? Ans = 0.0098
3. during production of a dosage form, the pharmaceutical company
normally expects to have 2% of the tablets in a batch to have less
than 95% of the labeled amount of a drug (defective). If 20 tablets are
randomly sampled from a batch, what is the probability of finding
three defective tablets? Ans = 0.0067
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62. 4. If the mean and standard deviation of the potency of a batch of
tablets are 50 and 5 mg, respectively, what proportion of the tablets
have a potency between 40 and 60 mg?
Ans =0.954
5. Serum sodium values for normal persons have a mean of 140 mEq/L
and a s.d. of 2.5. What is the probability that a person’s serum
sodium will be between 137 and 142 mEq/L?
Ans = 0.673
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63. End
Reference:
Ph’ceutical statistics- Practical and clinical
applications –Sanford Bolton
Fundamental of Statistics –S.C. Guptha
Net Source
of the topic