Question

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?

Answer 1

($13,300,$46,900)

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
  `1 - (1)/(k^2)` percent of data lies within 2 standard deviations of mean.
• For k = 3,

`1 -(1)/((3)^2) = 0.889 \approx 89\%`

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

`\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900`

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