Normal Distributions
Normal Probability听听
- Find听
-
- Area under the curve, probability, percentile, percent听
- Standard Normal Distribution听
-
- Mean = 0听听听听 SD = 1听
| Conditions | Probability | Calculator Input | Key Phrases | |
|---|---|---|---|---|
|
鈥� Continuous Data 鈥� Symmetrical 鈥� Mean in Middle 鈥� Data Separated by Standard Deviation 鈥� Area Adds to 1 |
鈥� P(X < x) 鈥� P(X 鈮� x) |
鈥� 2nd > Vars 鈥� 2: normalcdf |
鈥� Lower: -1E99 鈥� Upper: X 鈥� Mean: 渭 鈥� SD: 蟽 |
鈥� Less Than 鈥� At Most 鈥� Fewer Than 鈥� X or Less |
|
鈥� P(X > x) 鈥� P(X 鈮� x) |
鈥� Lower: X 鈥� Upper: 1E99 鈥� Mean: 渭 鈥� SD: 蟽 |
鈥� Greater Than 鈥� At Least 鈥� More Than 鈥� X or More |
||
|
鈥� P(X 鈮� x 鈮� Y) 鈥� P(X < x < Y) |
鈥� Lower: X 鈥� Upper: Y 鈥� Mean: 渭 鈥� SD: 蟽 |
鈥� Between | ||
|
鈥� P(x < X or x > Y) 鈥� P(x 鈮� X or x 鈮� Y) |
1 鈭� “Between” |
鈥� Tails 鈥� Less than X or Greater than Y |
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| Differs by Less |
鈥� Lower: 渭 鈭� X 鈥� Upper: 渭 + X 鈥� Mean: 渭 鈥� SD: 蟽 |
鈥� Differs by Less Than X 鈥� Differs by Fewer Than X |
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| Differs by More |
鈥� 1 – “Differs by Less” 鈥� 2 * normalcdf a tail |
鈥� Differs by Greater Than X 鈥� Differs by More Than X |
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invNorm听
- Find听
-
- z-score听
-
- Measurements听听
| Conditions | Direction | Calculator Input | Key Phrases | ||
|---|---|---|---|---|---|
| TI-83 | TI-84 | ||||
|
鈥� Continuous Data 鈥� Symmetrical 鈥� Mean in Middle 鈥� Data Separated by Standard Deviation 鈥� Area Adds to 1 |
Left |
鈥� 2nd > Vars 鈥� 3: invNorm |
p, 渭, 蟽 |
鈥� Area: p 鈥� Mean: 渭 鈥� SD: 蟽 鈥� Left |
鈥� To the Left 鈥� Bottom % 鈥� Percentile 鈥� Less Than |
| Right | (1-p), 渭, 蟽 |
鈥� Area: p 鈥� Mean: 渭 鈥� SD: 蟽 鈥� Right |
鈥� To the Right 鈥� Top % 鈥� More Than |
||
|
Between -z and z |
鈥�
1-p
2
, 0,1 Gives -z 鈥� z = -z × -1 |
鈥� Area: p 鈥� Mean: 0 鈥� SD: 1 鈥� Center |
鈥� Between 鈥� This is ONLY z-scores |
||
| Left -z and Right z |
鈥�
p
2
, 0,1 Gives -z 鈥� z = -z × -1 |
鈥� Area: 1-p 鈥� Mean: 0 鈥� SD: 1 鈥� Center |
鈥� Left of -z Plus Right of z 鈥� This is ONLY z-scores |
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鈥� Approximating a Binomial Distribution
o MUST follow the binomial distribution rules:
鈻� Fixed number of trials: n
鈻� Independent trials
鈻� Two outcomes: success and failure
鈻� Probability for success is the same every time: p
鈻� 饾憶饾憹 鈮� 10听听听听 饾憶(1鈭掟潙�)鈮�10
o 饾渿= 饾憶饾憹
o 蟽 = 鈭� np(1 鈭� p)
o MUST use continuity corrections
鈻� After the continuity correction, this is the same as normalcdf
| Examples of Continuity Correction | |||
|---|---|---|---|
| Statement | Symbol | Graph | Area |
|
鈥� At least 45 鈥� 45 or more 鈥� No fewer than 45 |
鈮�45 |
|
Right of 44.5 |
|
鈥� More than 45 鈥� Greater than 45 |
>45 |
| Right of 45.5 |
|
鈥� At most 45 鈥� No more than 45 |
鈮�45 |
|
Left of 45.5 |
|
鈥� Less than 45 鈥� Fewer than 45 |
<45 |
|
Left of 44.5 |
|
鈥� Exactly 45 鈥� Equal to 45 |
=45 |
|
Between 44.5 and 45.5 |
