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Questions and Answers
What is the value of X in the given equation, where V.Z = X - µ/σ?
What is the value of X in the given equation, where V.Z = X - µ/σ?
- 78.18
- 80.58
- 77.58
- 78.58 (correct)
What is the primary purpose of calculating the Z-value?
What is the primary purpose of calculating the Z-value?
- To determine the mode of a dataset
- To determine the standard deviation of a dataset
- To determine the mean of a dataset
- To determine the probability of occurrence of an event (correct)
What is the shape of the distribution curve when the data is skewed to the left?
What is the shape of the distribution curve when the data is skewed to the left?
- Asymmetrical with a longer left tail (correct)
- Asymmetrical with a longer right tail
- Symmetrical
- Bimodal
What is the difference between the normal distribution curve and the t-distribution curve?
What is the difference between the normal distribution curve and the t-distribution curve?
What is the formula to calculate the t-value?
What is the formula to calculate the t-value?
What is the area of the curve that is above 130 mmHg in a normal distribution curve with µ = 120 and σ = 10?
What is the area of the curve that is above 130 mmHg in a normal distribution curve with µ = 120 and σ = 10?
What is the importance of the Z-value in a normal distribution curve?
What is the importance of the Z-value in a normal distribution curve?
What is the shape of the distribution curve when the data is skewed to the right?
What is the shape of the distribution curve when the data is skewed to the right?
What is the value of the systolic blood pressure that divides the area under the curve into lower 97.5% and upper 2.5%?
What is the value of the systolic blood pressure that divides the area under the curve into lower 97.5% and upper 2.5%?
What is the primary difference between the normal distribution curve and the t-distribution curve?
What is the primary difference between the normal distribution curve and the t-distribution curve?
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Study Notes
Population Distribution
- Population distribution can be discrete, skewed, or normal (also known as continuous or Gaussian).
- Normal frequency distribution (NFD) is a continuous probability distribution with values ranging from -∞ to +∞.
- Each NFD is defined by its mean (µ) and standard deviation (σ).
Characteristics of Normal Frequency Distribution (NFD)
- Bell-shaped curve
- Symmetric
- Mean = mode = median
- The area under the curve represents all probabilities
- Data are clustered around the mean
- The distribution of data around the mean µ is described by units of standard deviation σ
Standard Normal Frequency Distribution (Z Distribution)
- Hypothetical curve where µ = 0 and σ = 1
- Z value is the fraction of standard deviation on the scale
- Z values range from -3 to +3
- The area represents the probability of occurrence of an event, and total area = 1 (represents 100%)
Importance of Z Value
- Decides whether an observation is normal or not
- Determines the probability of occurrence of an event in NFD curve
- Examples of determining probabilities using Z values are provided
Skewed Distribution
- Not symmetrical
- Can be negatively skewed (pulled to the left) or positively skewed (pulled to the right)
The t-Distribution
- Used to describe the distribution of means around the universal mean when the SD is unknown, but an estimate is available from a relatively small sample number
- For each sample size, there will be a special t-distribution curve
- t value = [𝑋 - µ] / SE
- Differences between NFD curve and t-distribution are:
- NFD doesn’t represent the sample number
- NFD is steep, while t-distribution is less steep and becomes less steep as n decreases
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