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Using z-scores If we convert a standard score (x-value) to a z-score, then we can use our standard normal distribution procedures. z x x z Example Men have a sitting heights that are normally distributed with a mean of 36.0 in. and a standard deviation of 1.4 in. The Honda Civic has a headroom of 39 in. What is the probability that a randomly selected man won’t fit in the Civic? If you want to design a car so that 97% of men can fit it in, what should the headroom be? Example Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. If you want to provide a warranty so that only 2% of the CD players will be replaced before the warranty expires, what is the time length of the warranty? Homework 5.3: 1, 7, 13, 17