An elevator has a placard stating that the maximum capacity is
1240 lb —88 passengers. So,
88 adult male passengers can have a mean weight of up to
1240 divided by 8 equals 155 pounds.1240/8=155 pounds.
If the elevator is loaded with
88
adult male passengers, find the probability that it is overloaded because they have a mean weight greater than
155
lb. (Assume that weights of males are normally distributed with a mean of
164 lb164 lb
and a standard deviation of
26 lb26 lb.)
Does this elevator appear to be safe?
The probability the elevator is overloaded is
nothing.
(Round to four decimal places as needed.)
Solution :
Given that ,
_{} = 164
_{} = / n = 26 / 8 = 9.19
P( > 155) = 1 - P( < 155)
= 1 - P[( - _{} ) / _{} < (155 - 164) / 9.19]
= 1 - P(z < -0.98)
= 1 - 0.1635
= 0.8365
No, there is a good chance that 8 randomly selected people will exceed the elevator capacity.
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