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−(x−μ)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 =x−μσ \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