The of 10 indicates that weekly income of 1100 is one standard deviation above

# The of 10 indicates that weekly income of 1100 is one

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The 𝑧 of 1.0 indicates that weekly income of \$1,100 is one standard deviation above the mean, and 𝑧 of -1.0 indicates that a \$900 income is one standard deviation below the mean The mean labour cost to repair a heat pump is \$90 with a standard deviation of \$22. Monte’s Plumbing completed repairs on two heat pumps this morning. The labour cost for the first was \$75, and it was \$100 for the second. Assume the distribution of labour costs follows the normal distribution. Compute 𝑧 values for each, and comment on your findings. Try This .... The Empirical Rule 1. Approximately 68% of observations will lie within ±1 standard deviation of the mean 2. About 95% of observations will lie within ±2 standard deviation of the mean 3. Practically all, 99.7% of observations will lie within ±3 standard deviation of the mean To verify the Empirical Rule: z of 1.00 = .3413 so .3413 * 2 = .6826 or about 68% z of 2.00 = .4772 so .4772 * 2 = .9544 or about 95% z of 3.00 = .4987 so .4987 * 2 = .9974 or about 99.7% The Empirical Rule Example: The Empirical Rule As part of its quality assurance program, the Autolite Battery Company conducts tests on battery life. For a particular D-cell alkaline battery, the mean life is 19 hours. The useful life of the battery follows a normal distribution with a standard deviation of 1.2 hours. a) About 68% of the batteries failed between what two values? b) About 95% of the batteries failed between what two values? c) Virtually all of the batteries failed between what two values? Example: The Empirical Rule a) About 68% of the batteries failed between what two values? 𝜇 + 1𝜎 = 19 ± 1.2 = 17.8 and 20.2 hrs b) About 95% of the batteries failed between what two values? 𝜇 + 2𝜎 = 19 ± 2(1.2) = 16.6 and 21.4 hrs c) Virtually all of the batteries failed between what two values? 𝜇 + 3𝜎 = 19 ± 3(1.2) = 15.4 and 22.6 hrs The mean of a normal probability distribution is 60; the standard deviation is 5. a) About what percent of the observations lie between 55 and 65? b) About what percent of the observations lie between 50 and 70? c) About what percent of the observations lie between 45 and 75? Try This .... 