The Standard Normal Distribution Quiz

PDF page 288: The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical calculation of probabilities. Take a moment and substitute zero and one in the appropriate places in the above formula and you can see that the equation collapses into one that can be much more easily solved using integral x − μ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from calculus. The transformation z = σ a known normal distribution with known mean μ and known standard deviation σ. The z-score tells how many standard deviations a particular x is away from the mean.

PDF page 288: The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical calculation of probabilities. Take a moment and substitute zero and one in the appropriate places in the above formula and you can see that the equation collapses into one that can be much more easily solved using integral x − μ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from calculus. The transformation z = σ a known normal distribution with known mean μ and known standard deviation σ. The z-score tells how many standard deviations a particular x is away from the mean.

PDF page 288: The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical calculation of probabilities. Take a moment and substitute zero and one in the appropriate places in the above formula and you can see that the equation collapses into one that can be much more easily solved using integral x − μ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from calculus. The transformation z = σ a known normal distribution with known mean μ and known standard deviation σ. The z-score tells how many standard deviations a particular x is away from the mean.

PDF page 288: The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical calculation of probabilities. Take a moment and substitute zero and one in the appropriate places in the above formula and you can see that the equation collapses into one that can be much more easily solved using integral x − μ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from calculus. The transformation z = σ a known normal distribution with known mean μ and known standard deviation σ. The z-score tells how many standard deviations a particular x is away from the mean.

PDF page 288: If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score for a particular x is: x – μ z = σ The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero.

PDF page 288: If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score for a particular x is: x – μ z = σ The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero.

PDF page 289: x – μ 17 – 5 z = = = 2 σ 6

PDF page 289: This means that x = 17 is two standard deviations (2σ) above or to the right of the mean μ = 5.

PDF page 289: This means that x = 1 is 0.67 standard deviations (–0.67σ) below or to the left of the mean μ = 5.

PDF page 289: • About 68% of the x values lie between –1σ and +1σ of the mean μ (within one standard deviation of the mean).

PDF page 289: • The z-scores for +2σ and –2σ are +2 and –2, respectively.

PDF page 289: values lie between –1σ = (–1)(6) = –6 and 1σ = (1)(6) = 6 of the mean 50. The values 50 – 6 = 44 and 50

PDF page 289: + 6 = 56 are within one standard deviation from the mean 50. The z-scores are –1 and +1 for 44 and 56, respectively.