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3. A car manufacturer is interested in conducting a study to estimate the mean stopping distance for a new type
of brakes when used in a car that is traveling at 60 miles per hour. These new brakes will be installed on cars
of the same model and the stopping distance will be observed. The cost of each observation is $100. A budget
of $12,000 is available to conduct the study and the goal is to carry it out in the most economical way possible.
Preliminary studies indicate that s �� 12 feet for stopping distances.
(a) Are sufficient funds available to estimate the mean stopping distance to within 2 feet of the true mean
stopping distance with 95% confidence?
Explain your answer.
(b) A regulatory agency requires a 95% level of confidence for an estimate of mean stopping distance that
is within 2 feet of the true mean stopping distance. The car manufacturer cannot exceed the budget of
$12,000 for the study. Discuss the consequences of these constraints.

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