Experts have predicted that approximately 1 in12 tractor-trailer units will be involved in...

Experts have predicted that approximately 1 in12 tractor-trailer units will be involved in an accident this year. One reason for this is that 1 in 3 tractor-trailer units has an imminently hazardous mechanical condition, probably related to the braking system on the vehicle. A survey of 50 tractor-trailer units passing through a weighing station confirmed that 19 had a potentially serious braking system problem.

a. Do the binomial assumptions hold?

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b. Can a normal approximation to the binomial be applied here to get a confidence interval for π?

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c. Give a 95% confidence interval for π using these data. Is the interval informative? What could be done to decrease the width of the interval, assuming  remained the same?