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Non-Standard Normal Distribution quiz

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  • What are the mean and standard deviation of the standard normal distribution?
    The mean (μ) is zero and the standard deviation (σ) is one.
  • What equation do you use to convert a value from a nonstandard normal distribution to a z-score?
    You use z = (x - μ) / σ.
  • If a normal distribution has μ = 20 and σ = 5, what is the z-score for x = 10?
    The z-score is (10 - 20) / 5 = -2.
  • Why do we convert nonstandard normal values to z-scores?
    We convert them so we can use the standard normal table or calculator to find probabilities.
  • What does a z-score represent in a normal distribution?
    It represents how many standard deviations a value is from the mean.
  • How do you find the probability that a value is less than a certain x in a nonstandard normal distribution?
    First, convert x to a z-score, then use the z-table to find the probability.
  • What is the formula to find an x value given a z-score in a nonstandard normal distribution?
    The formula is x = z * σ + μ.
  • If 5% of values are below a certain x in a normal distribution with μ = 20 and σ = 5, what is the first step to find x?
    First, find the z-score that corresponds to a cumulative probability of 0.05.
  • What is the z-score associated with the lowest 5% of a standard normal distribution?
    The z-score is approximately -1.64.
  • How do you use the z-score to find the corresponding x value in a nonstandard normal distribution?
    Multiply the z-score by the standard deviation and add the mean: x = z * σ + μ.
  • What is the x value below which 5% of commute times fall if μ = 20 and σ = 5?
    The x value is x = (-1.64) * 5 + 20 = 11.8.
  • What does the area to the left of a z-score represent in a normal distribution?
    It represents the probability that a value is less than the corresponding x value.
  • Why is it useful to standardize a nonstandard normal distribution?
    Standardizing allows us to use standard normal tables and methods to solve probability problems.
  • What is the general process for finding probabilities in a nonstandard normal distribution?
    Convert x to a z-score, then use the standard normal table to find the probability.
  • How do you solve for x when given a probability in a nonstandard normal distribution?
    Find the z-score for the probability, then use x = z * σ + μ to solve for x.