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29 January, 10:32

Suppose the dealer incentive per vehicle for honda's acura brand in 2012 is thought to be bell-shaped and symmetrical with a mean of $2500 anda standard deviation of $300. Based in this information,

what interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within?

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  1. 29 January, 10:40
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    From $1600 to $3400.

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean = 2500

    Standard deviation = 300

    What interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within?

    By the Empirical Rule, 99.7% fall within 3 standard deviations frow the mean. So

    From 2500 - 3*300 = 1600 to 2500 + 3*300 = 3400.
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