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Non-Standard Normal Distribution quiz

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  • What is the equation used to transform a nonstandard normal variable into a standard normal variable?
    The equation is (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.
  • What does a z-score represent in a normal distribution?
    A z-score measures how many standard deviations a data point is from the mean.
  • How do you find the probability that a randomly selected value is less than a certain x in a nonstandard normal distribution?
    First, convert x to a z-score using (x - μ) / σ, then use a z-table or calculator to find the probability.
  • What are the mean and standard deviation for a standard normal distribution?
    The mean (μ) is 0 and the standard deviation (σ) is 1.
  • How do you interpret a z-score of -2 in a standard normal distribution?
    It means the value is two standard deviations to the left of the mean.
  • What is the probability associated with a z-score of -2 in a standard normal distribution?
    The probability is approximately 0.023, or 2.3%.
  • How do you find the x value associated with a given probability in a nonstandard normal distribution?
    First, find the z-score for the probability, then use x = zσ + μ to calculate the corresponding x value.
  • If the mean commute time is 20 minutes and the standard deviation is 5 minutes, what is the z-score for a commute time of 10 minutes?
    The z-score is (10 - 20) / 5 = -2.
  • What is the formula to find x when you know the z-score, mean, and standard deviation?
    The formula is x = zσ + μ.
  • How do you find the z-score associated with a probability of 5% in a standard normal distribution?
    Use a z-table or calculator to find the z-score, which is approximately -1.64.
  • What x value corresponds to the lowest 5% of commute times if μ = 20 and σ = 5?
    The x value is x = (-1.64)(5) + 20 = 11.8 minutes.
  • What does transforming a nonstandard normal distribution to a standard normal distribution allow you to do?
    It allows you to use standard z-tables and calculators to find probabilities and values.
  • What is the first step when finding an x value for a given probability in a nonstandard normal distribution?
    First, find the z-score associated with the given probability.
  • How do you solve for x if you know the probability, mean, and standard deviation?
    Find the z-score for the probability, then use x = zσ + μ to solve for x.
  • What percentage of people have commute times less than 11.8 minutes if μ = 20 and σ = 5?
    About 5% of people have commute times less than 11.8 minutes.