In: Statistics and Probability
An elevator has a placard stating that the maximum capacity is 1580 lblong dash 10 passengers. So, 10 adult male passengers can have a mean weight of up to 1580 divided by 10 equals 158 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 158 lb. (Assume that weights of males are normally distributed with a mean of 168 lb and a standard deviation of 33 lb .) Does this elevator appear to be safe? The probability the elevator is overloaded is nothing . (Round to four decimal places as needed.) Does this elevator appear to be safe? A. Yes, 10 randomly selected people will always be under the weight limit. B. Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity. C. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity. D. No, 10 randomly selected people will never be under the weight limit
Solution:
Given:
An elevator has a placard stating that the maximum capacity is 1580 lbl- 10 passengers.
The weights of males are normally distributed with a mean of 168 lb and a standard deviation of 33 lb.
The elevator is loaded with 10 adult male passengers.
Find the probability that it is overloaded because they have a mean weight greater than 158 lb.
That is find:
Find z score for
Thus we get:
Look in z table for z = -0.9 and 0.06 and find corresponding area.
P( Z< -0.96) = 0.1685
thus
The probability the elevator is overloaded is 0.8315
Does this elevator appear to be safe?
Since the probability the elevator is overloaded is 0.8315 is very high, so it is not safe.
Thus correct answer is:
C. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.