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21 May, 08:57

A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what percentage of cars are driving less than 45 mi/hr? (Round to the nearest tenth of a percent)

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  1. 21 May, 12:34
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    Answer: the percentage of cars that are driving less than 45 mi/hr is 2.3%

    Step-by-step explanation:

    Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = speeds of cars

    µ = mean speed

    σ = standard deviation

    From the information given,

    µ = 55 mi/hr

    σ = 5 mi/hr

    The probability that a car is driving less than 45 mi/hr is expressed as

    P (x < 45)

    For x = 45

    z = (45 - 55) / 5 = - 2

    Looking at the normal distribution table, the probability corresponding to the z score is 0.023

    Therefore, the percentage of cars that are driving less than 45 mi/hr is

    0.023 * 100 = 2.3%
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