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The average age of passenger train cars is 19.4 years. If the distribution of ages is...

The average age of passenger train cars is 19.4 years. If the distribution of ages is normal and 14% of the cars are older than 22.7 years, find the standard deviation.

Math   Statistics-And-Probability   
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Answer #1

solution:

Let X be the normal random variable representing the age of car

Given that

The average age of cars = = 19.4 years

Probability of cars older than 22.7 years = P(X>22.7) = 0.14

= 0.14

   = 0.14

= 0.14

= 0.14

= 0.86

   = 1.0805 [ use standard Normal distribution table]

   = 3.3 / 1.0805

   = 3.05

Required Standard Deviation () = 3.05 years

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