The time required for an automotve center to complete an col change service on a

Question

The time required for an automotve center to complete an col change service on an automobile approximately iollows a normal distribution, with a mean of 17 minutes and a standard deviation of 3 minutes (a) The automotive center guarantees customers that the service will take no longer than 20 minutes Ifit does take langer, the customer vwill receive the service for half-price. What percent of customers receive the service for half-price? (b) the automotive center does not want to give the discount to more than 5% o its customers, how long should i make the guaranteed time i t? % (a) The percent of customers that receve the service for half-pnces Round to two decimal places as needed ) (b) The guaranleed time limit is minutes (Round up to the nearest integer as needed Enter your answer in each of the answer boxes Related Bloss SAT -Free Practice Tests ess than or equal to ulduz anee we cant look ie up exar 3202 | Matthew % ReponPrevention: The Way to Your A in Statisties

Explanation / Answer

a) probability that service will take longer then 20 minutes =P(X>20)=P(Z>(20-17)/3) =P(Z>1)=0.1587~ 15.87%

b) for 95 percentile ; z=1.6449

hence guarantee limit =mean +z*std deviaiton =~ 22 minutes ( rounding it up)

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