An elevator has a placard stating that the maximum capacity is 2475 lb —15 passengers. So, 15 adult male passengers can have a mean weight of up to 2475/15=165 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. (Assume that weights of males are normally distributed with a mean of 167 lb and a standard deviation of 35 lb.) Does this elevator appear to be safe?
The probability the elevator is overloaded is -- round four decimal places
Solution :
Given that ,
_{} = 167
_{} = / n = 35 / 15
P( > 165) = 1 - P( < 165)
= 1 - P[( - _{} ) / _{} < (165 - 167) / 35 / 15 ]
= 1 - P(z < -0.22)
= 1 - 0.4129
= 0.5871
No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.
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