Question

The Department of Health requires that the ambulance service reaches 85% of life-threatening calls within 8 minutes. The management of a medical emergency response unit collects data on its ambulances’ response times to life threatening incidents in the past month. The data distribution is bell shaped with mean equal to 7 minutes and standard deviation equal to 1.5 minutes. Answer the following questions: a. State an appropriate probability distribution model for the response times. b. What percentage of the response times is between 6 and 7 minutes? c. What percentage of the response times is more than 8 minutes? d. Check if the emergency response unit meets the standards of the Department of Health. e. What parameters of the distribution should be changed, and how, to further improve the performance of the unit? f. If the mean is reduced to 6.5 minutes what percent of calls is reached within 8 minutes? (assume std deviation remains 1.5 min) g. If the standard deviation is reduced to 0.9 minute what percent of calls is reached within 8 minutes? (assume mean remains 7).

Answer 1

a) The response time's distribution is bell shaped which means the response times follow an approximately normal distribution with mean = 7 minutes and standard deviation = 1.5 minutes.
b)

The probability that the response times will be between 6 and 7 minutes is

Hence, 24.76% of the response times are between 6 and 7 minutes.

c) The probability that the response times will be greater than 8 minutes is

Hence, 25.24% of the response times are greater than 8 minutes.

d) The probability that the response time is less than or equal to 8 minutes is

= 1 - The probability that the response time is greater than 8 minutes

= 1 - 0.2524 = 0.7476

The emergency response unit reaches only 74.76% of the calls within 8 minutes. Hence, it doesn't meet the standards of the department of health.

e) In order to improve the performance of the unit, the mean response time should be less than 7 or the standard deviation of the response times should be less.

f) If the new reduced mean is 6.5, the new percentage will be

Hence, if the mean is reduced to 6.5minutes, 84.13% of the response times will be less than 8 minutes which meets the standard of the Department of health.

g) If the standard deviation is reduced to 0.9, the new percentage will be

In this case, 86.67% of the calls is reached within 8 minutes.

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