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MATH104- Ch. 12 Statistics- part 1CNormal Distribution
Normal Distribution
•
Excerpt of Normal Chart– see p. 720
Z-score percentile Z-score percentile
-4.0 0.003 0.0 50.00
-3.0 0.13 0.5 69.15
-2.0 2.28 1.0 84.13
-1.0 15.87 2.0 97.72
-0.5 30.85 3.0 99.87
4.0 99.997
Find the given probabilities
Easiest examples• P(z<1)=
• P(z<2)=
• P(z< -2)=
• P(z<1.5)=
Harder examples
• Recall P(z<1)= Try P(z>1)=
• Recall P(z<2)= Try P(z>2)=
• P(z>1.3)=
• P(z> -2.4)=
Find the given probabilities• P( - 1<z<1)=
• P( -2<z<2)=
• P( -1.5<z<1.5)=
• P(1.4 < z < 2.3)=
• P( -1.8<z< 2.3)=
• P(- 2.1<z< -0.7)=
Normal Distribution Problems– Given x, find z, and then find P
• Example #1:• Scores on a standardized test are normal with
the mean = μ= 100 and the pop st dev =σ= 10. Create a normal curve to picture this example.
μ = 100 , σ = 10 Find the probably that scores are:
• Lower than 100
• Lower than 110
• Greater than 110
• Between 90 and 110
• Between 80 and 120…
Continued… Find the probability that scores are:
• Lower than 115
• Greater than 115
• Lower than 108
Calculate z using the formula, and then find probability
• Lower than 93
• Between 93 and 108
• Hint: z =
Example #2-snowfall
• Assume snowfall amounts are normally distributed with mean μ =140, st dev = σ = 20. Find the probability that the amount is:
• Less than 180 inches
• Greater than 162 inches
• Between 134 and 174 inches
Ex 3: Heights- mean = 48 , st dev= 4
•
Margin of error (p. 725)—
if a statistic is obtained from a random sample of size n, there is a 95% probability that it lies within of the true populations statistic, where is called the margin of error.
If 1100 people were surveyed about a politician, and 61%
thought favorably of this person, the margin of error would be: So, there is a 95% probability that the true population percentage
is between: