What is a Normal distribution with a mean of 0 and variance of 1 called?
Standard Normal distribution
Match the Normal distribution property with its description:
Mean ↔️ The average value
Variance ↔️ Measure of spread
Symmetry ↔️ Symmetric around the mean
Total Area ↔️ Equals 1
What is the Normal distribution defined by?
Mean and variance
The probability density function of the Normal distribution is given by f(x)
What does the variance measure in the Normal distribution?
Spread
The Normal distribution is symmetric around its mean
The total area under the Normal distribution curve is equal to 1.
What is a Normal distribution with a mean of 0 and variance of 1 called?
Standard Normal distribution
Increasing the mean of a Normal distribution shifts the curve to the right
A larger standard deviation in a Normal distribution results in a flatter and wider curve.
What are the two parameters that define the Standard Normal distribution?
Mean of 0 and variance of 1
What is a Normal distribution with a mean of 0 and variance of 1 called?
Standard Normal distribution
The Normal distribution is defined by its mean and variance.
The probability density function of the Normal distribution is given by f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{ - \frac{1}{2}(\frac{x - \mu}{\sigma})^{2}}</latex>, where μ represents the mean
Match the property of the Normal distribution with its description:
Mean ↔️ The average value
Variance ↔️ Measure of spread
Symmetry ↔️ Symmetric around the mean
Total Area ↔️ Total area under the curve
What does the mean of a Normal distribution determine?
Center of the curve
What is the Normal distribution also known as?
Gaussian distribution
The mean, median, and mode of a Normal distribution are equal.
The Normal distribution is defined by its mean and standard deviation.
What is the probability density function of the Normal distribution?
f(x)=σ2π1e−2σ2(x−μ)2
The Normal distribution is a continuous probability distribution.
The Normal distribution is defined by its mean and variance.
The standard deviation of a Normal distribution determines the spread
Increasing the mean of a Normal distribution shifts the curve to the right.
What type of curve represents the Normal distribution graphically?
Bell-shaped
The mean of a Normal distribution is located at the peak
Steps to calculate probabilities using the Normal distribution:
1️⃣ Standardize the value using the z-score
2️⃣ Use a z-table or calculator
3️⃣ Find the cumulative probability
What formula is used to calculate the z-score?
z=σx−μ
Standardizing a Normal distribution results in a mean of 0 and a standard deviation of 1.
If x=75, μ=70, and σ=5, the z-score is 1
What does a z-score of 1 indicate in terms of standard deviations?
One above the mean
What is the average value of the data in a Normal distribution called?
Mean
The mean of a Normal distribution shifts the curve along the x-axis
What are the two key parameters of the Normal distribution?
Mean and standard deviation
The mean of a Normal distribution shifts the entire curve along the x-axis.
The standard deviation of a Normal distribution measures the spread or variability of the data
What happens to the Normal distribution curve when the mean is increased?
Shifts to the right
What are the two parameters of the Normal distribution?
Mean and standard deviation
The mean represents the average value of the data in a Normal distribution.
What happens to the Normal distribution curve when the standard deviation is increased?