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21 July, 23:05

The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. Nationwide, the distribution of average response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be in order to qualify for the special safety award

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  1. 22 July, 00:15
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    Answer: in order to qualify, the time must be at least 15.93 minutes

    Step-by-step explanation:

    Let x be a random variable representing the average response times of fire departments to fire calls. Since it follows a normal distribution, we will determine the z score by applying the formula,

    z = (x - µ) / σ

    Where

    x = sample mean

    µ = population mean

    σ = population standard deviation

    From the information given,

    µ = 12.8 minutes

    σ = 3.7 minutes

    in order to qualify for the special safety award, the probability value would be to the right of the z score corresponding to 80%

    The z score corresponding to 80% on the normal distribution table is 0.845

    Therefore,

    0.845 = (x - 12.8) / 3.7

    0.845 * 3.7 = x - 12.8

    3.13 = x - 12.8

    x = 12.8 + 3.13 = 15.93
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