3. The time required for Speedy Lube to complete an oil change follows a normal

Question

3. The time required for Speedy Lube to complete an oil change follows a normal distribution, with a mean of 20 minutes and tomobile approximately ce on an au a standard deviation of 4 minutes. a. What proportion of Speedy Lube oil hanges are completed in less tha n 23.5 minutes ? b. What proportion of Speedy Lube oil changes are completed in more than 20.5 minutes? c. What is the probability that a randomly selected Speedy Lube customer will have his/her oil changed between 20.5 and 23.5 minutes ?

Explanation / Answer

Mean is 20 and s is 4

a) P(x<23.5) =P(z<(23.5-20)/4)=P(z<0.88)

from normal distribution table we get 0.8106

b) P(x>20.5)=P(z>(20.5-20)/4)=P(z>0.13) or 1-P(z<0.13) , from normal table it is 1-0.5517=0.4483

c) P(20.5<x<23.5)=P(z<23.5)-P(z<20.5)=0.8106-0.5517=0.2589

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