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Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 89% of new car prices to fall within?

Respuesta :

Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

  • According to  theorem atleast [tex]1 - \dfrac{1}{k^2}[/tex]  percent of data lies within 2 standard deviations of mean.
  • For k = 3,

[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]

Thus, 89% of data lies within three standard deviation of mean.

[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

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