Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours. . Let x = the time needed to fix a furnace. Required:
a. What is the probability that it takes the repairman more than 7 hours to fix a furnace?
b. Find the probability that a randomly selected furnace repair requires less than 3 hours.
c. Find the 30th percentile of furnace repair times.
d. The longest 25% of repair furnace repairs take at least how long? (In other words: Find the minimum time for the longest 25% of repair times.) What percentile does this represent?
e. Find the mean and standard deviation

a

b

c

d

e

Mean

Standard deviation  

Step-by-step explanation:

From the question we are told that

  The amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours

Generally the probability that it takes the repairman more than 7 hours to fix a furnace is mathematically represented as

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Generally the probability that a randomly selected furnace repair requires less than 3 hours. is mathematically represented as

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Generally the 30th percentile of furnace repair times is mathematically represented as

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Generally the time taken for the longest 25% of furnace repair is mathematically evaluated as

Here making use of the because we are considering duration that fall with the top

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Generally the mean is mathematically represented as

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Generally the standard deviation is mathematically represented as

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