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    Normal Distribution Problem - College of Business at Bradley University in Peoria, Illinois

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    A study by professors in the College of Business at Bradley University in Peoria, Illinois, revealed that the response time to 911 emergency calls was 4.8 minutes, with a standard deviation of 1.2 minutes. It was assumed that response times were normally distributed. The mayor of Peoria wanted to reduce mean response time enough so that 40 percent of all calls were answered within 3.5 minutes.

    It was estimated that the cost of patrol cars, fire units, and personnel would be $575,000 for every reduction of 30 seconds. The necessary revenue was to be raised by a property tax. However, the mayor felt that the tax burden should be borne only by those homes above $70,000 in assessed value. Homes average $45,000 in value, with a standard deviation of $15,110. The mayor felt that an average of an additional $96 could be raised for each home in Peoria over $70,000. There are 42,000 homes in the Peoria city limits. Based on these constraints, is her plan feasible?

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    Solution Preview

    In this problem, we are to find out the mean so that 40% of calls are answered within 3.5 minutes (standard deviation assumed to be 1.2mins and does not change)

    Z value for 40% = -0.25335 (from normal tables)

    We have -0.25335 = (3.5 - ...

    Solution Summary

    The solution determines if a plan for the College of Business at Bradley University in Peoria is feasible.