A random sample of 100 automobile owners in the state of Virginia shows that an

Question

A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers. Assume the distribution of measurements to be approximately normal

a) Construct a 95% confidence interval for the average number of kilometers an automobile is driven annually in Virginia.

b) What can we assert with 95% confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

Explanation / Answer

Soln: Given: n = 100, = 3,900 km,x = 23,500 km

a) 99% confidence interval From Table , z/2 = z.025 = 1.96

_x - z/2 /n < µ < x + z/2 /n

23,500 – 1.96(3,900)/100 < µ < 23,500 + 1.96(3,900)/100

22735.6 < µ < 24,264.4

b) Error 1.96(3,900)/100

764.4 km

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