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Suppose that the average speed of cars on a busy section of a local highway was normally distributed with a mean of 65 mph and standard deviation of 4 mph. What is the probability that the speed of a random car in this data set was less than 53 mph?

0.025
0.0015
0.16
0.475

Respuesta :

Answer: Choice B)  0.0015

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Explanation:

  • mu = 65 = population mean
  • sigma = 4 = population standard deviation

Let's convert x = 53 to its corresponding z score

z = (x-mu)/sigma

z = (53-65)/4

z = -12/4

z = -3

This indicates we're 3 standard deviations below the mean.

Recall that the Empirical Rule states that roughly 99.7% of the data items in a normal distribution are within 3 standard deviations of the mean. That leaves 100% - 99.7% = 0.3% outside this range. This small percentage is the combined percentage in both tails. Take half of this to find the amount in the left tail only.

(0.3%)/2 = 0.15%

This then converts to 0.0015 when we move the decimal point 2 spots to the left.

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