4 The average labor charge for automobile mechanics is 116 p

4.) The average labor charge for automobile mechanics is $116 per hour. The standard deviation is $9. Using Chebyshev’s theorem, find the percentage of data values that will fall in the range of $100-130. Show your work!  

8.) A recent poll by the American Automobile Club found that 73.6% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that

-At least one will be worried about aggressive drivers on the road?

-At most two will be worried about aggressive drivers on the road?

10.)    The average national ACT score is 22. If we assumed a bell-shaped distribution and a standard deviation of 3.4, within what limits would you expect approximately

A.) 95% of the scores to fall?

B.) 68% of the scores to fall?

C.) 99.7% of the scores to fall?

Solution

4.

As

k = (x - u)/sigma

where u = mean, sigma = standard deviation

For x = 100

k1 = (100 - 116)/9 = -1.777777778

For x = 130,

k2 = (130-116)/9 = 1.555555556

Hence, by Chebyshev\'s theorem, at least

1 - 1/(2 k1^2) - 1/(2 k2^2)

= 1 - 1/(2*1.777777778^2) - 1/(2*1.555555556^2)

= 0.635164222

= 63.52% LIE WITHIN 100-130 [ANSWER]

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