Question

An elevator has a placard stating that the maximum capacity is 1610 lblong dash10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1610 divided by 10 equals 161 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 161 lb.​ (Assume that weights of males are normally distributed with a mean of 171 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?

Answer 1

Solution :

mean = = 171

standard deviation = = 28

n = 10

= = 171

= / n = 28 / 10 = 8.85

P( > 161) = 1 - P( < 161)

= 1 - P[( - ) / < (161 - 171) / 8.85]

= 1 - P(z < -1.13)

Using z table,    

= 1 - 0.1292

= 0.8708

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