2.4.3 Normal distribution

    Cards (55)

    • 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)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\mu 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)=f(x) =1σ2πe(xμ)22σ2 \frac{1}{\sigma \sqrt{2\pi}} e^{ - \frac{(x - \mu)^{2}}{2\sigma^{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=z =xμσ \frac{x - \mu}{\sigma}
    • Standardizing a Normal distribution results in a mean of 0 and a standard deviation of 1.
    • If x=x =75 75, μ=\mu =70 70, and σ=\sigma =5 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?
      Becomes wider and flatter