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2. The speeds of cars on the highway have a mean of 65 mph with a standard deviation of 5 mph.
a) What percentage of cars averaged less than 62mph?

Respuesta :

Edufirst

Answer:

  • a) 27.43%

Explanation:

To find the percentage of cars averaged less than 62 mph calculate the corresponding z-score and use a standard normal cumulative probability table

1. Z-score

     [tex]Z-score=\dfrac{x-\mu}{\sigma}[/tex]

  • x is the specific value of the random variable: 62mph
  • μ is the mean of the population: 65mph
  • σ is the standard deviation of the population: 5mph

Substitute and calculate

       [tex]Z-score=\dfrac{62-65}{5}=-0.600[/tex]

2. Use of the table.

The percentage of cars that averaged less than 62mph is given by the area under the curve to the left of z = -0.600.

From a standard normal cumulative probability table, the probability of z being less than -0.600 (which is equal to the probability of z being greater than 0.600) is 0.2743, which is 27.43%.

Thus, the conclusion is that 27.43% of the cars averaged less than 62mph.

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