Question

An elevator has a placard stating that the maximum capacity is 1580 lb   - 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.

Answer 1

Solution :

Given that ,

= 168

= / n = 33 / 10 = 10.44

P( > 158) = 1 - P( < 158)

= 1 - P[( - ) / < (158 - 168) / 10.44 ]

= 1 - P(z < -0.96)   

= 1 - 0.1685

= 0.8315

correct option is = C

No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.