7. 0.75 points The Body Paint, an automobile body paint shop, has determined tha

Question

7. 0.75 points The Body Paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 50 minutes to 1: hours. a. What is the probability that the painting time of a single automobile will be less than or equal to one hour? ANSWER: b. What is the probability that the painting time of a single automobile will be more than 75 minutes? ANSWER: c. Determine the mean painting time. ANSWER: (report your answer to 4 decimal places, using conventional rounding rules) (report your answer to 4 decimal places, using conventional rounding rules) report your answer to 2 decimal places, using conventional rounding rules) Determine the standard deviation of painting time. ANSWER: conventional rounding rules) report your answer to 2 decimal places, using Check my work

Explanation / Answer

Ans:

Given that

uniform distribution with

a=50 min and b=1.5 hr=90 min

For uniform distribution:

P(T<=t)=(t-a)/(b-a)=(t-50)/(90-50)=(t-50)/40

a)P(T<=60)=(60-50)/40=0.2500

b)P(T>75)=1-P(T<=75)=1-(75-50)/40=1-(25/40)=0.3750

c)Mean painting time=(a+b)/2=(50+90)/2=70.00

d)variance=(b-a)^2/12=(90-50)^2/12=40^2/12

standard deviation=sqrt(40^2/12)=40/sqrt(12)=11.55

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