The Body Paint, an automobile body paint shop, has determined that the painting

Question

The Body Paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and thai the required time ranges between 45 minutes to 1 1/2 hours a. Give a mathematical expression for the probability density function. b. What is the probability that the painting time will be less than or equal to one hour? c. What is the probability that the painting time will be more than 50 minutes? d. Determine the expected painting time and its standard deviation 2.

Explanation / Answer

here for uniform distribution paramter a =45 and b =90 minutes

a)pdf f(x) =1/(b-a) =1/(90-45) =1/45

b)probability of painting time will be less than or equal to 1 hour(60 minutes) =P(X<=60)=(x-a)/(b-a) =(60-45)/(90-45)

=15/45 =1/3 =0.3333

c)probability of painting time will be more than 50 minutes =P(X>50) =1-P(X<50)=1-(50-45)/(90-45)=1-5/45

=0.8889

d)

expected time =(a+b)/2 =(45+90)/2 =67.5

std deviation =(b-a)/(12)1/2 =(90-45)/(12)1/2 =12.99

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