Question

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

Answer 1

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.